Exploring Predictors of COVID Crime Shifts

The lockdown and social distancing measures that were brought in throughout the world to tackle COVID in 2020 have had a significant, widespread effect on crime. In this notebook, I use public London crime data on robbery and burglary to examine where this “COVID crime shift” was strongest, and whether any specific drivers or correlates can be identified.

Our findings suggest that the relative change in burglary and robbery trends during “lockdown” in April and May 2020 was heavily affected by local characteristics: areas with a high residential population saw teh sharpest decreases in burglary (likely due to a reduction in available targets) while the reduction in robberies instead seem to be driven by geographic features and proxy indicators of deprivation (potentially suggesting more available targets for robbery in communities least able to work for from).

The primary purpose of this exercise was to learn R - I’ve previously worked entirely in Python, which is more than sufficient 99% of the time, but has at times proved a blocker when I want to tackle some more experimental geospatial methods or tools geared towards the academic community. With that in mind, this is likely to be a little messy, and I’ll aim to condense my main lessons into a blog post in the future. The models are not heavily tuned (aiming to explore correlates rather than provide accurate predictions) and certain predictors are likely to correlate with each other, and as such likely do not imply direct causations.

Resources I’ve used

Tasks

  1. Ingest burglary and robbery data and assign to MSOA
  2. Predict trend by MSOA
  3. Identify COVID effect/error by MSOA
  4. Model

Data

In this exercise, I’m using three years of Metropolitan Police Service data from data.police.uk - I’ve downloaded these manually rather than using their API.

1. Ingest burglary and robbery data and assign to MSOA

Unlike Python has the benefit of being “focused” - it’s primaryily a tool for academics/scientists, rather than a programming language. That means the eco-system is refreshingly helpful: at first glance, there is one primary IDE, one package library, and it all works. Unlike Python, most libraries are imported globally, and that works okay…mostly

MSOAs are geographical units specifically designed for analysis, and to be comparable: they all have an average population of just over 8,000.

# Data manipulation, transformation and visualisation
library(tidyverse)
# Nice tables
# Simple features (a standardised way to encode vector data ie. points, lines, polygons)
# Spatial objects conversion
library(sp) 
library(tmap) 
# Colour palettes
library(RColorBrewer) 
# More colour palettes
library(viridis)
#ggplot organiastion
library(ggpubr)


library(rgdal)  # input/output, projections

library(lubridate) #date and time

#random forest and metrics
library(randomForest)
require(caTools)
library(DALEX)
library(dplyr)


library(corrr)

Importing data from CSV files behaves quite similarly to Python. To build our process, we’ll start by taking one month of crime data, exploring it, and writing all our steps for automation.

test_df <- read.csv("crimes/2018-01/2018-01-metropolitan-street.csv")
test_df
Error in gregexpr(calltext, singleline, fixed = TRUE) : 
  regular expression is invalid UTF-8
Error in gregexpr(calltext, singleline, fixed = TRUE) : 
  regular expression is invalid UTF-8

Our crime is categories according to the Home Office major crime types, and like Python, we can list them all through the “unique” function. Here I’ll be focusing on robbery and burglary: two crime types that are heavily reliant on encountering victim’s in public spaces, and as such should be affected by the “COVID effect”.

unique(test_df["Crime.type"])

To avoid this getting particularly computationally intensive, let’s write a function to pull out robberies and burglaries, and assign them a specific MSOA. Then we can iterate over all our months and get monthly counts for each offence type.

subset_df <- filter(test_df, Crime.type=="Burglary" | Crime.type=="Robbery")
subset_df

Our single month of data contains 10,501 crimes.

There are R/Python quirks that will take some getting used to. While in Python, most columns can be referenced through their string name ([“name”]), R seems somewhat fussier. Other than that, the move from one to another is largely intuitive.

We now need to link this to our spatial data. We use the MSOA borders provided by MOPAC, and use the UK National Grid coordinate system. Police.uk does not use that system, so we’ll need to reproject our crime data.

lsoa_borders <- st_read("msoa_borders/MSOA_2011_London_gen_MHW.tab", crs=27700)
Reading layer `MSOA_2011_London_gen_MHW' from data source `C:\Users\andre\Dropbox\Data Projects\Covid_crime_shift\msoa_borders\MSOA_2011_London_gen_MHW.tab' using driver `MapInfo File'
Simple feature collection with 983 features and 12 fields
geometry type:  MULTIPOLYGON
dimension:      XY
bbox:           xmin: 503574.2 ymin: 155850.8 xmax: 561956.7 ymax: 200933.6
projected CRS:  OSGB 1936 / British National Grid
lsoa_borders
Simple feature collection with 983 features and 12 fields
geometry type:  MULTIPOLYGON
dimension:      XY
bbox:           xmin: 503574.2 ymin: 155850.8 xmax: 561956.7 ymax: 200933.6
projected CRS:  OSGB 1936 / British National Grid
First 10 features:
    MSOA11CD                 MSOA11NM   LAD11CD              LAD11NM   RGN11CD RGN11NM UsualRes HholdRes ComEstRes PopDen Hholds AvHholdSz
1  E02000001       City of London 001 E09000001       City of London E12000007  London     7375     7187       188   25.5   4385       1.6
2  E02000002 Barking and Dagenham 001 E09000002 Barking and Dagenham E12000007  London     6775     6724        51   31.3   2713       2.5
3     10045    10033        12   46.9   3834       2.6
4  E02000004 Barking and Dagenham 003 E09000002 Barking and Dagenham E12000007  London     6182     5937       245   24.8   2318       2.6
5  E02000005 Barking and Dagenham 004 E09000002 Barking and Dagenham E12000007  London     8562     8562         0   72.1   3183       2.7
6      8791     8672       119   50.6   3441       2.5
7  E02000008 Barking and Dagenham 007 E09000002 Barking and Dagenham E12000007  London    11569    11564         5   81.5   4591       2.5
8  E02000009 Barking and Dagenham 008 E09000002 Barking and Dagenham E12000007  London     8395     8376        19   87.4   3212       2.6
9  E02000010 Barking and Dagenham 009 E09000002 Barking and Dagenham E12000007  London     8615     8615         0   76.8   3292       2.6
10 E02000011 Barking and Dagenham 010 E09000002 Barking and Dagenham E12000007  London     6187     6086       101   38.8   2289       2.7
                         geometry
1  MULTIPOLYGON (((532135.1 18...
2  MULTIPOLYGON (((548881.6 19...
3  MULTIPOLYGON (((549102.4 18...
4  MULTIPOLYGON (((551550 1873...
5  MULTIPOLYGON (((549099.6 18...
6  MULTIPOLYGON (((549819.9 18...
7  MULTIPOLYGON (((548171.4 18...
8  MULTIPOLYGON (((546855 1863...
9  MULTIPOLYGON (((549618.8 18...
10 MULTIPOLYGON (((550244.1 18...

Unlike our previous dataframes, this isn’t “tidy” (due to a slightly different format containing geographical data)

plot(lsoa_borders)
plotting the first 9 out of 12 attributes; use max.plot = 12 to plot all

Before we can link our crimes to MSOA, we’ll need to ensure identical coordinate systems, but before we do that, we’ll need to erase any missing values.

#count missing values in the longitude column
sum(is.na(subset_df["Longitude"]))
[1] 82

As such, we have 82 crimes with no geographic identifiers, which we remove from our analysis.

clean_df <- subset_df[!rowSums(is.na(subset_df["Longitude"])), ]
clean_df

We can now convert our crime data to spacial data, using our longitude and latitude coordinates - this allows us to quickly plot our data, and confirm it looks right.


subset_spatial <- st_as_sf(clean_df, coords = c("Longitude", "Latitude"), 
                      crs = 4326, remove = FALSE)

subset_spatial
Simple feature collection with 10419 features and 12 fields
geometry type:  POINT
dimension:      XY
bbox:           xmin: -0.492381 ymin: 51.28683 xmax: 0.273434 ymax: 51.68564
geographic CRS: WGS 84
First 10 features:
                                                           Crime.ID   Month                 Reported.by                Falls.within Longitude Latitude
1  628e0d673aa1b6a70479342a64b02884499df85b18dcd63cc9bff3cff9f704bc 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
2  f8e9db16dca534a83493198a838567aa5adc9dd56496edc2fff5bb4c62b8303e 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
3  cc34822074b130f141f16d02fdb2d500c86e22ae18324b43a3231b381af3f45c 2018-01 Metropolitan Police Service Metropolitan Police Service  0.135554 51.58499
4  10de581c3cd0a8c9b970824cd7589d13148d63a70b3115d95ef6c24dc0bd2c3b 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
5  50ad5d2dfea24afec9e17218db62b3d29786775db1060634ae7d4a6e7cafc3ff 2018-01 Metropolitan Police Service Metropolitan Police Service  0.127794 51.58419
6  95abc6eb0b755c9250d19bbe0062fcd4a509b701964d89667401c9dc96ca257d 2018-01 Metropolitan Police Service Metropolitan Police Service  0.138439 51.57850
7  035cc894d732addb5009148d8e163e6360094cfe451f621348f1c0419b9cbc77 2018-01 Metropolitan Police Service Metropolitan Police Service  0.138439 51.57850
8  495cac920dcf9e0e4927074e8ac307f17d340f01c69e434c4a3721df017cd342 2018-01 Metropolitan Police Service Metropolitan Police Service  0.139479 51.57974
9  48234e70cbc22265ee7968da92df1ca72f83b45414cce486ec2203daa4e59fa2 2018-01 Metropolitan Police Service Metropolitan Police Service  0.135119 51.57849
10 3f4ba20780987c37816ff34fd0f7760cf503b2e648777f84ee0104432cb01d66 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140452 51.58110
                       Location LSOA.code                 LSOA.name Crime.type                         Last.outcome.category Context                  geometry
1    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary                       Offender sent to prison      NA POINT (0.140035 51.58911)
2    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary Investigation complete; no suspect identified      NA POINT (0.140035 51.58911)
3          On or near Rose Lane E01000027 Barking and Dagenham 001A   Burglary                     Status update unavailable      NA POINT (0.135554 51.58499)
4    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary                     Status update unavailable      NA POINT (0.140035 51.58911)
5         On or near Hope Close E01000028 Barking and Dagenham 001B   Burglary                     Status update unavailable      NA POINT (0.127794 51.58419)
6     On or near Geneva Gardens E01000029 Barking and Dagenham 001C   Burglary Investigation complete; no suspect identified      NA  POINT (0.138439 51.5785)
7     On or near Geneva Gardens E01000029 Barking and Dagenham 001C   Burglary                     Status update unavailable      NA  POINT (0.138439 51.5785)
8   On or near Yew Tree Gardens E01000029 Barking and Dagenham 001C   Burglary                     Status update unavailable      NA POINT (0.139479 51.57974)
9     On or near Portland Close E01000029 Barking and Dagenham 001C   Burglary                     Status update unavailable      NA POINT (0.135119 51.57849)
10 On or near Pedestrian Subway E01000030 Barking and Dagenham 001D    Robbery Investigation complete; no suspect identified      NA  POINT (0.140452 51.5811)
plot(subset_spatial)
plotting the first 9 out of 12 attributes; use max.plot = 12 to plot all

Success! That looks faintly promising. Now, let’s figure out how to re-project.


latlong = "+init=epsg:4326"
ukgrid = "+init=epsg:27700"
subset_osgb <- st_transform(subset_spatial, ukgrid)
GDAL Message 1: +init=epsg:XXXX syntax is deprecated. It might return a CRS with a non-EPSG compliant axis order.
subset_osgb
Simple feature collection with 10419 features and 12 fields
geometry type:  POINT
dimension:      XY
bbox:           xmin: 504499 ymin: 155908 xmax: 557677 ymax: 200168
projected CRS:  OSGB 1936 / British National Grid
First 10 features:
                                                           Crime.ID   Month                 Reported.by                Falls.within Longitude Latitude
1  628e0d673aa1b6a70479342a64b02884499df85b18dcd63cc9bff3cff9f704bc 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
2  f8e9db16dca534a83493198a838567aa5adc9dd56496edc2fff5bb4c62b8303e 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
3  cc34822074b130f141f16d02fdb2d500c86e22ae18324b43a3231b381af3f45c 2018-01 Metropolitan Police Service Metropolitan Police Service  0.135554 51.58499
4  10de581c3cd0a8c9b970824cd7589d13148d63a70b3115d95ef6c24dc0bd2c3b 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
6  95abc6eb0b755c9250d19bbe0062fcd4a509b701964d89667401c9dc96ca257d 2018-01 Metropolitan Police Service Metropolitan Police Service  0.138439 51.57850
7  035cc894d732addb5009148d8e163e6360094cfe451f621348f1c0419b9cbc77 2018-01 Metropolitan Police Service Metropolitan Police Service  0.138439 51.57850
8  495cac920dcf9e0e4927074e8ac307f17d340f01c69e434c4a3721df017cd342 2018-01 Metropolitan Police Service Metropolitan Police Service  0.139479 51.57974
9  48234e70cbc22265ee7968da92df1ca72f83b45414cce486ec2203daa4e59fa2 2018-01 Metropolitan Police Service Metropolitan Police Service  0.135119 51.57849
10 3f4ba20780987c37816ff34fd0f7760cf503b2e648777f84ee0104432cb01d66 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140452 51.58110
                       Location LSOA.code                 LSOA.name Crime.type                         Last.outcome.category Context                geometry
1    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary                       Offender sent to prison      NA   POINT (548349 189976)
2    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary Investigation complete; no suspect identified      NA   POINT (548349 189976)
3          On or near Rose Lane E01000027 Barking and Dagenham 001A   Burglary                     Status update unavailable      NA POINT (548052 189507.9)
4    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary                     Status update unavailable      NA   POINT (548349 189976)
5         On or near Hope Close E01000028 Barking and Dagenham 001B   Burglary                     Status update unavailable      NA   POINT (547517 189404)
6     On or near Geneva Gardens E01000029 Barking and Dagenham 001C   Burglary Investigation complete; no suspect identified      NA   POINT (548273 188793)
7     On or near Geneva Gardens E01000029 Barking and Dagenham 001C   Burglary                     Status update unavailable      NA   POINT (548273 188793)
8   On or near Yew Tree Gardens E01000029 Barking and Dagenham 001C   Burglary                     Status update unavailable   Burglary                     Status update unavailable      NA   POINT (548043 188785)
10 On or near Pedestrian Subway E01000030 Barking and Dagenham 001D    Robbery Investigation complete; no suspect identified      NA   POINT (548404 189086)

We now run a “spatial join”: assigning an MSOA to each of our crimes, based on the MSOA border map they are within, and combining these as one table.

crime_with_msoa <- st_join(subset_osgb, lsoa_borders["MSOA11CD"])
crime_with_msoa
Simple feature collection with 10419 features and 13 fields
geometry type:  POINT
dimension:      XY
bbox:           xmin: 504499 ymin: 155908 xmax: 557677 ymax: 200168
projected CRS:  OSGB 1936 / British National Grid
First 10 features:
                                                           Crime.ID   Month                 Reported.by                Falls.within Longitude Latitude
1  628e0d673aa1b6a70479342a64b02884499df85b18dcd63cc9bff3cff9f704bc 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
2  f8e9db16dca534a83493198a838567aa5adc9dd56496edc2fff5bb4c62b8303e 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
3  cc34822074b130f141f16d02fdb2d500c86e22ae18324b43a3231b381af3f45c 2018-01 Metropolitan Police Service Metropolitan Police Service  0.135554 51.58499
4  10de581c3cd0a8c9b970824cd7589d13148d63a70b3115d95ef6c24dc0bd2c3b 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140035 51.58911
5  50ad5d2dfea24afec9e17218db62b3d29786775db1060634ae7d4a6e7cafc3ff 2018-01 Metropolitan Police Service Metropolitan Police Service
6  95abc6eb0b755c9250d19bbe0062fcd4a509b701964d89667401c9dc96ca257d 2018-01 Metropolitan Police Service Metropolitan Police Service  0.138439 51.57850
7  035cc894d732addb5009148d8e163e6360094cfe451f621348f1c0419b9cbc77 2018-01 Metropolitan Police Service Metropolitan Police Service  0.138439 51.57850
8  495cac920dcf9e0e4927074e8ac307f17d340f01c69e434c4a3721df017cd342 2018-01 Metropolitan Police Service Metropolitan Police Service  0.139479 51.57974
9  48234e70cbc22265ee7968da92df1ca72f83b45414cce486ec2203daa4e59fa2 2018-01 Metropolitan Police Service Metropolitan Police Service  0.135119 51.57849
10 3f4ba20780987c37816ff34fd0f7760cf503b2e648777f84ee0104432cb01d66 2018-01 Metropolitan Police Service Metropolitan Police Service  0.140452 51.58110
                       Location LSOA.code                 LSOA.name Crime.type                         Last.outcome.category Context  MSOA11CD
1    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary                       Offender sent to prison      NA E02000002
2    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary Investigation complete; no suspect identified      NA E02000002
3          On or near Rose Lane E01000027 Barking and Dagenham 001A   Burglary                     Status update unavailable      NA E02000002
4    On or near Beansland Grove E01000027 Barking and Dagenham 001A   Burglary                     Status update unavailable      NA E02000002
5         On or near Hope Close E01000028 Barking and Dagenham 001B   Burglary                     Status update unavailable      NA E02000002
6     On or near Geneva Gardens E01000029 Barking and Dagenham 001C   Burglary Investigation complete; no suspect identified      NA E02000002
7     On or near Geneva Gardens E01000029 Barking and Dagenham 001C   Burglary                     Status update unavailable      NA E02000002
8   On or near Yew Tree Gardens E01000029 Barking and Dagenham 001C   Burglary                     Status update unavailable      NA E02000002
9     On or near Portland Close E01000029 Barking and Dagenham 001C   Burglary                     Status update unavailable      NA E02000002
10 On or near Pedestrian Subway E01000030 Barking and Dagenham 001D    Robbery Investigation complete; no suspect identified      NA E02000002
                  geometry
1    POINT (548349 189976)
2    POINT (548349 189976)
3  POINT (548052 189507.9)
4    POINT (548349 189976)
5    POINT (547517 189404)
6    POINT (548273 188793)
7    POINT (548273 188793)
8    POINT (548341 188933)
9    POINT (548043 188785)
10   POINT (548404 189086)

That has worked: each crime is now assigned to an MSOA. We can now group our table by count of MSOA, to obtain the monthly count of

msoa_list<- crime_with_msoa %>%
  group_by(MSOA11CD, Crime.type) %>%
  summarize(count_by_msoa = n())
`summarise()` has grouped output by 'MSOA11CD'. You can override using the `.groups` argument.
msoa_list
Simple feature collection with 1722 features and 3 fields
geometry type:  GEOMETRY
xmin: 504499 ymin: 155908 xmax: 557677 ymax: 200168
projected CRS:  OSGB 1936 / British National Grid

We now have a count for each, and we can remove the geometry data before automating our process.

msoa_pivot_tibble <- as_tibble(msoa_list)
msoa_pivot_tibble <- msoa_pivot_tibble[0:3]
msoa_pivot_tibble
NA

As a final stage prior to processing the rest of our data, we will fill any missing msoa/month combinations with a “0”, to ensure consistent trends.

#creating a df with all msoa names, for robbery and burglary
msoa_zero_df_robbery <- unique(as_tibble(lsoa_borders)["MSOA11CD"])
msoa_zero_df_burglary <- unique(as_tibble(lsoa_borders)["MSOA11CD"])

#adding our crime type column 
msoa_zero_df_burglary["Crime.type"] = "Burglary"
msoa_zero_df_robbery["Crime.type"] = "Robbery"

#Creating a "count" column identical to our pivot, and filling it with 0
msoa_zero_df_robbery["count_by_msoa"] = as.numeric(0)

#combine both
duplicate_concat <- rbind(msoa_zero_df_robbery, msoa_zero_df_burglary)
#add our duplicates to our original table
df_with_dups <- rbind(msoa_pivot_tibble, duplicate_concat)


dup_filters <- duplicated(df_with_dups[0:2])


#bring it all back together
monthly_df <- filter(df_with_dups, !dup_filters)
monthly_df

#select the first unique value of months in the original dataframe
month <- unique(test_df["Month"])[1,1]
monthly_df["Month"] <- month
monthly_df
NA

we now have our basic functionality to create a time series for both crime types, by MSOA - a count of each type, and the month.

I can now bring all my previous work together into a function, which we can use to automate the process.

#quick initial function to generate our MSOA borde spatial frame, to avoid it sitting in the initial frame and gobbling loads of memory.
generate_msoa_borders <- function(file){
  msoa_borders <- st_read(file, crs=27700)
  return(msoa_borders)
}

make_month_pivot <- function(file){
  #define our CRS
  latlong = "+init=epsg:4326"
  ukgrid = "+init=epsg:27700"
  #read our crime from the file
  test_df <- read.csv(file)
  #select only our target crime types
  subset_df <- filter(test_df, Crime.type=="Burglary" | Crime.type=="Robbery")
  #remove any rows with a long/lat coordinate
  clean_df <- subset_df[!rowSums(is.na(subset_df["Longitude"])), ]
  #generate a spatial df
  subset_spatial <- st_as_sf(clean_df, coords = c("Longitude", "Latitude"), 
                      crs = 4326, remove = FALSE)
  #reproject to uk grid coords
  subset_osgb <- st_transform(subset_spatial, ukgrid)
  #spatially join to assign to an MSOA
  crime_with_msoa <- st_join(subset_osgb, msoa_borders["MSOA11CD"])
  #summarise by count of MSOA
  msoa_list<- crime_with_msoa %>%
    group_by(MSOA11CD, Crime.type) %>%
  #return to a non-geographic msoa
  msoa_pivot_tibble <- as_tibble(msoa_list)
  msoa_pivot_tibble <- msoa_pivot_tibble[0:3]
  #creating a df with all msoa names, for robbery and burglary
  msoa_zero_df_robbery <- unique(as_tibble(msoa_borders)["MSOA11CD"])
  msoa_zero_df_burglary <- unique(as_tibble(msoa_borders)["MSOA11CD"])
  msoa_zero_df_burglary["Crime.type"] = "Burglary"
  msoa_zero_df_robbery["Crime.type"] = "Robbery"
  #Creating a "count" column identical to our pivot, and filling it with 0
  msoa_zero_df_burglary["count_by_msoa"] = as.numeric(0)
  duplicate_concat <- rbind(msoa_zero_df_robbery, msoa_zero_df_burglary)
  df_with_dups <- rbind(msoa_pivot_tibble, duplicate_concat)
  #creating a filter for duplicates columns, which should ignore the first instance
  dup_filters <- duplicated(df_with_dups[0:2])
  monthly_df <- filter(df_with_dups, !dup_filters)
  month <- unique(test_df["Month"])[1,1]
  monthly_df["Month"] <- month
  return(monthly_df)
}

We now have a rudimentary tooling pipeline, which we can iterate over our subfolders to aggregate our data (in hindset, I probably should have explored the API options).

#create empty dataframe to bring together our data
empty_df <- tibble(
MSOA11CD = "", 
Crime.type= "",
count_by_msoa= "",
Month= ""
)

#re-ingest our MSOA data
msoa_borders <- generate_msoa_borders("msoa_borders/MSOA_2011_London_gen_MHW.tab")

Our function will iterate over each file, add them to our empty table, until each is complete (and we have a single, aggregated file)

subfiles <- list.files(path = "crimes", recursive=T)

for (file in subfiles){
  folder_subdir <- "crimes/"
  #concatenate to get our total subfolder directory - hacky but will work here.
  sub_path <- paste(folder_subdir, file, sep="")
  monthly_df <- make_month_pivot(sub_path)
}
empty_df

We now have a combined dataframe of 71,848 rows, from January 2018 through December 2020.

unique(empty_df["Month"])

From a practical perspective, that was slightly more painful than I expected - I’m not sure if data-wrangling is less intuitive in R, or it’s just practice, but it’s noticeable how easy use cases are less easily accessible as tutorials (probably due to the different user base )

#saving file to CSV
#write.csv(empty_df,"msoa_crime_matrix.csv")

2. Predict trend by MSOA

Visualisation and Exploration

With our data now cleaned and aggregated, we can focus on the more interesting part - forecasting our “expected” pandemic crime, and examining how much it diverges from our “actual” crime.

empty_df <- read.csv("msoa_crime_matrix.csv")
empty_df <- empty_df[2:70848,2:5]
empty_df

Before going any further, let’s use this to explore and visualise the distribution of robbery and burglary across time and space during our “pre-pandemic” period, in March 2020 - based on London mobility indicators, this is when movement accross London began to be heavily affected, and the disruption was most notable in April

London mobility data

burglary_df<-empty_df

#add a "1" so our month can be converted to a full date
burglary_df$DateString <- paste(burglary_df$Month, "-01", sep="")

#convert to date format
burglary_df$DateClean <- ymd(burglary_df$DateString)

#filter out only burglary prior to the pandemic
burglaryExplore <- filter(burglary_df,  DateClean < "2020-03-01" & Crime.type=="Burglary")

burglaryExplore

Looking at the aggregate counts of burglary across London, a visual observation suggests yearly trends (which we’ll have to consider in our forecast), which sharp peaks during the Winter months and the lowest numbers in summer (when the days are longest).

burglary_by_month <- burglaryExplore %>%
  group_by(DateClean) %>%
  summarize(total_burglaries = sum(count_by_msoa))

ggplot(burglary_by_month, aes(x=DateClean, y=total_burglaries)) +
  geom_line()

To observe how crime counts are distributed in space, let’s map both counts by MSOA. As previously mentioned, MSOAs are designed to be comparable units, at least from a population perspective - we don’t need to produce per population rates.

burglary_by_msoa <- burglaryExplore %>%
  group_by(MSOA11CD) %>%
  summarize(total_burglaries = sum(count_by_msoa))

burglary_map <- left_join(lsoa_borders, burglary_by_msoa, by = "MSOA11CD")

pal <- brewer.pal(5,"BuGn")


  tm_fill(col = "total_burglaries", title = "Total Burglary Count by MSOA", style="quantile", palette="BuGn") +
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")

robbery_df<-empty_df

robbery_df$DateString <- paste(robbery_df$Month, "-01", sep="")
robbery_df$DateClean <- ymd(robbery_df$DateString)
robberyExplore <- filter(robbery_df,  DateClean < "2020-03-01" & Crime.type=="Robbery")

robbery_by_msoa <- robberyExplore %>%
  group_by(MSOA11CD) %>%
  summarize(total_robberies = sum(count_by_msoa))

robbery_map <- left_join(lsoa_borders, robbery_by_msoa, by = "MSOA11CD")

pal <- brewer.pal(5,"BuGn")


robbery_map <-tm_shape(robbery_map) +
  tm_fill(col = "total_robberies", title = "Total Robbery Count by MSOA", style="quantile", palette="BuGn") +

tmap_arrange(burglary_map, robbery_map, nrow = 2)

We notice that robbery is noticeably more concentrated in central London, with burglary remaining quite common across the city. That said, there are also obvious spatial patterns here - these crimes are clustered in certain geographies.

Modelling

We can now begin the forecasting process. To design our process, we’ll start by focusing on a single MSOA - the first in our dataset, E02000001, or the City of London.

single_msoa_df <- filter(empty_df, MSOA11CD == "E02000001" & Crime.type=="Burglary")

single_msoa_df$DateString <- paste(single_msoa_df$Month, "-01")


single_msoa_df

From a forecasting/time-series perspective, this is a very small dataset - 36 monthly observations. We will be shrinking this further to only 26 by focusing on data prior to March 2020, when the COVID crime impact is felt. This significantly limits our forecasting options, and will impact accuracy, if we treat each MSOA in isolation - we could explore some sort of Vector Autoregressive Model to limit this, but given that we’re then going to be exploring the error of all our models in aggregation, this isn’t crucial. Our focus is on models that we can accurately deploy without needing to tune each of them individually, and that can capture the seasonal trend, and generate reliable predictions on our limited dataset.

Given these limitations, I’ve opted for the Prophet algorith. While it’s more opaque than a auto-arima or VAR model, it works well with monthly data, and extracting seasonal trends. It also requires very little tuning.

As such, we’ll extract our “training set” prior to March, and start forecasting.


training_set <- filter(single_msoa_df, DateClean < "2020-03-01")

training_df <- tibble(
  y=training_set$count_by_msoa
)
training_df
library(prophet)
m <- prophet(training_df)

For now, we’ll forecast on a 6 month horizon - we obviously wouldn’t expect it to be accurate that far into the future.

future <- make_future_dataframe(m, periods = 6, freq = 'month')


forecast <- predict(m, future)

plot(m, forecast)

As we can see, the model seems consistent on a short horizon, and gets very wide as it goes further into the future. More importantly however, it has extracted a yearly seasonal compontent - the summer decrease we identified previously - as well as a long term trend.


prophet_plot_components(m, forecast)

These predictions seem far-fetched, but remember we will be observing a London wide error rate. As such, we must now isolate our “pandemic period” - which we define as April and May 2020 - and compare the predicted crime counts to the actual crime counts to obtain a metric of our “COVID crime shift”, or our error rate.



forecast$Month <- month(forecast$ds)
forecast$Year <- year(forecast$ds)


this_year <- filter(forecast, Year > 2019)
peak_pandemic <- filter(this_year, Month== 4 | Month== 5 )

predictionPivot <- peak_pandemic %>%
  group_by(Month) %>%


single_msoa_df$MonthNum <- month(single_msoa_df$DateClean)
single_msoa_df$YearNum <- year(single_msoa_df$DateClean)

this_year_actual <- filter(single_msoa_df, YearNum > 2019)
peak_pandemic_actual <- filter(this_year_actual, MonthNum== 4 | MonthNum== 5 )

actual_burglary <- sum(peak_pandemic_actual$count_by_msoa)
pred_burglary <- sum(predictionPivot$predicted_burglary)

error <- actual_burglary - pred_burglary
percentage_error <- error / pred_burglary 

print("Burglary Count")
[1] "Burglary Count"
print(actual_burglary)
print("Predicted")
[1] "Predicted"
print(pred_burglary)
[1] 7.625019
print("Actual Error")
print(error)
[1] -6.625019
print("Percentage Error")
[1]
print(percentage_error)
[1] -0.8688528

In this MSOA, our model predicted nearly 8 burglaries would occur in these two months, based on pre-pandemic trends. In reality, 1 took place - a large error rate, suggesting a strong “COVID effect”.

This process can now be replicated for every MSOA in London, to obtain this metric for each MSOA.

msoa_error_tibble

Our process has completed: we have a “COVID shift” measure for all of London.

3. Measuring Local COVID Crime Shifts

We now need to use our forecasts to measure the “error” - this should provide an indication of the “COVID Crime Shift”, or how much the actual crime diverted from the previous forecasts.

I explored various avenues for this: the ideal solution would be a relative rate of the error, as MSOAs with large crime numbers will likely generate large errors, and so a rate would be ideal, though this is complicated by our erratic prediction and mix of positive and negative numbers.

Our final solution has explored two options: - the absolute error number - the relative error once the crime and predictions have been transformed (by adding 50)

We visualise and describe these statistics first to ensure they appear sensible.

#write_csv(msoa_error_tibble, "msoa_error_table2.csv")
msoa_error_tibble <- read_csv("msoa_error_table2.csv")
#msoa_error_tibble<- msoa_error_table[2:980,]

msoa_error_tibble <- msoa_error_tibble[2:980, ]

msoa_error_tibble <- left_join(msoa_error_tibble, robbery_by_msoa, by = "MSOA11CD")
msoa_error_tibble <- left_join(msoa_error_tibble, burglary_by_msoa, by = "MSOA11CD")

msoa_error_tibble$RPDRobbery <- (msoa_error_tibble$robberyActual - msoa_error_tibble$robberyPredicted)/((msoa_error_tibble$robberyPredicted + msoa_error_tibble$robberyActual)/2)

msoa_error_tibble$robberyActualShifted <- msoa_error_tibble$robberyActual + 50
msoa_error_tibble$robberyPredictedShifted <- msoa_error_tibble$robberyPredicted + 50



msoa_error_tibble$burglaryActualShifted <- msoa_error_tibble$burglaryActual + 50
msoa_error_tibble$burglaryPredictedShifted <- msoa_error_tibble$burglaryPredicted + 50
print("Burglary Error")
[1] "Burglary Error"
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
-97.191 -12.870  -5.271  -6.090   2.111  48.727 
print("Burglary Relative Error")
[1] "Burglary Relative Error"
summary(msoa_error_tibble$RPDburglaryShifted)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-0.81266 -0.20689 -0.08826 -0.07976  0.03612  1.29467 
[1] "Robbery Error"
summary(msoa_error_tibble$robberyError)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
  -2.150   -3.840    2.205   25.564 
print("Robbery Relative Error")
[1] "Robbery Relative Error"
summary(msoa_error_tibble$RPDRobberyShifted)
    Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
-1.45491 -0.11808 -0.04081 -0.04876  0.04309  0.62020 

As we can see, the average London MSOA experienced a negative COVID crime shift for both burglary and robbery, but this is far from equally distributed - at the extremes, some areas actually see large increases on our predicted values.

library(ggpubr)
Loading required package: ggplot2
Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     
burg_hist <- ggplot(msoa_error_tibble, aes(x=burglaryError)) + geom_histogram()
rob_hist <-ggplot(msoa_error_tibble, aes(x=robberyError)) + geom_histogram()
burg_r_hist <- ggplot(msoa_error_tibble, aes(x=RPDburglaryShifted)) + geom_histogram()
rob_r_hist <- ggplot(msoa_error_tibble, aes(x=RPDRobberyShifted)) + geom_histogram()
scatter <- ggplot(msoa_error_tibble, aes(x = RPDRobberyShifted, y = RPDburglaryShifted)) +
  geom_point()

r_scatter <- ggplot(msoa_error_tibble, aes(x = robberyError, y = burglaryError)) +
  geom_point()

ggarrange(rob_hist, burg_hist, rob_r_hist, burg_r_hist,scatter, r_scatter, ncol=2, nrow=3 )
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Our shifted relative error rate seems to function as intended: while there are still outliers, they are more concentrated than they are for the pure error term, and the overall distribution is more focused, while still indicating the direction and relative strength of our COVID effect.

Let’s map this effect visually, and see if any particular areas stand out.

#re-ingest our geographic MSOA borders
msoa_borders <- st_read("msoa_borders/MSOA_2011_London_gen_MHW.tab", crs=27700)
Reading layer `MSOA_2011_London_gen_MHW' from data source `' using driver `MapInfo File'
Simple feature collection with 983 features and 12 fields
geometry type:  MULTIPOLYGON
dimension:      XY
bbox:           xmin: 503574.2 ymin: 155850.8 xmax: 561956.7 ymax: 200933.6
projected CRS:  OSGB 1936 / British National Grid
geographic_error_map <- left_join(msoa_borders, msoa_error_tibble, by = "MSOA11CD")

burg_map <- tm_shape(geographic_error_map) +
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")
rob_map <-tm_shape(geographic_error_map) +
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")


burg_map_rate <- tm_shape(geographic_error_map) +
  tm_fill(col = "RPDRobberyShifted", title = "Robbery Error Relative", palette="-PuOr")+
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")
rob_map_rate <-tm_shape(geographic_error_map) +


tmap_arrange(burg_map, rob_map, burg_map_rate, rob_map_rate , nrow = 2, ncol=2)

It’s hard to identify any obvious effect visually, but we do notice that while central London sees some very strong reductions, it also sees some increases. Conversely, the outskirts of London (notably to the south and West) are a near continuous area of large decreases. The effect does vary by offence type, but the pattern seen in South and West London appears broadly consistent.

4. Identifying Correlates and Modelling

We’ve identified that the COVID crime effect was felt unequally accross London, and varies by offence type. To finalise our project, we will be linking our data to demographic data provided by MOPAC, and aiming to use it to identify correlates to our “covid shift”, and hopefully build models disentangling the effect.

library(readxl)
#ingest ATLAS
msoa_atlas <- read_excel("msoa_atlas/msoa-data.xls")
New names:
* `House Prices Sales 2011` -> `House Prices Sales 2011...129`
* `House Prices Sales 2011` -> `House Prices Sales 2011...130`
geographic_msoa_matrix <- left_join(geographic_error_map, msoa_atlas, by = "MSOA11CD")

#convert to tibble
msoa_matrix_tbl <- as_tibble(geographic_msoa_matrix)


#select only numeric data
msoa_matrix_numeric <-dplyr::select_if(msoa_matrix_tbl, is.numeric)
msoa_matrix_numeric

Having now ingested and linked our data, we begin by exploring the factors most highly correlated with our relative error rates.


corr_df <- correlate(dplyr::select_if(msoa_matrix_tbl, is.numeric), quiet = TRUE)

options(scipen=999)

Starting by our relative robbery error, a few interesting correlates stand out: - road traffic casualties - burglary numbers - the number of dwellings with no usual residents, and the number of commercial residents - households with no cars - the age composition of the area - general deprivation indicators (such as the proportion of households with central heating)

#show only correlates with an absolute value higher than 0.2
#filter(dplyr::select(corr_df[order(corr_df$RPDRobberyShifted),] , term, RPDRobberyShifted), RPDRobberyShifted < -0.2 | RPDRobberyShifted > 0.2)
#filter(dplyr::select(corr_df[order(corr_df$RPDRobberyShifted),] , term, RPDRobberyShifted), RPDRobberyShifted < -0.2 | RPDRobberyShifted > 0.2)
high_corr_rob <- filter(dplyr::select(corr_df, term, RPDRobberyShifted), RPDRobberyShifted < -0.15 | RPDRobberyShifted > 0.15)

high_corr_rob[order(high_corr_rob$RPDRobberyShifted),]
NA

The correlations for burglary are weaker - only a few have an absolute value higher than 0.2 - but a few stand out: - households with no residents - high robbery numbers - house prices


high_corr_burg <- filter(dplyr::select(corr_df, term, RPDburglaryShifted), RPDburglaryShifted < -0.15 | RPDburglaryShifted > 0.15)

high_corr_burg[order(high_corr_burg$RPDburglaryShifted),]
NA

These correlates suggest we can model this shift - this is likely to prove more reliable for robbery (where the correlations are stronger), and seem linked to usual resident population(as measured by household composition), deprivation (through various proxy indicators such as central heating presence or housing type), and general crime patterns (through total burglary and robbery numbers)

We will take two approaches for modelling: a simple regression (to identify strong links) and random forest regressors (to identify non-linear associations)

Simple Regression

We begin through the use of simple OLS regression. This is a linear model that has large limitations for modelling complex relationships, but can be an effective first step, effectively with a few transformations.

R does not cope well with blank spaces in terms, so we’ll extract and rename our key correlates.




msoa_copy <- msoa_matrix_numeric

names(msoa_copy)[names(msoa_copy) == "Dwelling type (2011) Household spaces with no usual residents"] <- "DwellingNoResidents"
names(msoa_copy)[names(msoa_copy) == "House Prices Median House Price (£) 2010"] <- "MedianHousePrice"
names(msoa_copy)[names(msoa_copy) == "Dwelling type (2011) Flat, maisonette or apartment"] <- "FlatAprt"
names(msoa_copy)[names(msoa_copy) == "Qualifications (2011 Census) Schoolchildren and full-time students: Age 18 and over"] <- "fullTimeStudents"
names(msoa_copy)[names(msoa_copy) == "Car or van availability (2011 Census) No cars or vans in household"] <- "NoCars"
names(msoa_copy)[names(msoa_copy) == "Ethnic Group (2011 Census) Other ethnic group"] <- "OtherEthnicGroup"
names(msoa_copy)[names(msoa_copy) == "Central Heating (2011 Census) Households with central heating (%)"] <- "CentralHealingPercent"

Let’s now extract these to a separate dataframe, remove any missing values, and provide some quick summary statistics to identify any obvious concerns.


feature_df <- dplyr::select(msoa_copy, RPDburglaryShifted, RPDRobberyShifted, total_burglaries, total_robberies, DwellingNoResidents, MedianHousePrice, FlatAprt, fullTimeStudents, NoCars, OtherEthnicGroup, CentralHealingPercent, AvHholdSz, ComEstRes)
feature_df <- drop_na(feature_df, RPDburglaryShifted, RPDRobberyShifted)
feature_df
summary(feature_df)
 RPDburglaryShifted RPDRobberyShifted  total_burglaries total_robberies   DwellingNoResidents    FlatAprt      fullTimeStudents     NoCars    
 Min.   :-0.81266   Min.   :-1.45491   Min.   :  46.0   Min.   :   2.00   Min.   :  14.0      Min.   : 137625   Min.   :  54.0   Min.   : 122.0   Min.   : 185  
 1st Qu.:-0.20689   1st Qu.:-0.11808   1st Qu.: 121.0   1st Qu.:  29.00   1st Qu.:  59.0      1st Qu.: 222500   1st Qu.: 830.5   1st Qu.: 305.5   1st Qu.: 796  
 Median :-0.08826   Median :-0.04081   Median : 159.0   Median :  53.00   Median :  86.0      Median : 465.0   Median :1256  
 Mean   :-0.07976   Mean   :-0.04876   Mean   : 175.5   Mean   :  78.53   Mean   : 123.4      Mean   : 310710   Mean   :1798.2   Mean   : 539.5   Mean   :1382  
 3rd Qu.: 0.03612   3rd Qu.: 0.04309   3rd Qu.: 205.0   3rd Qu.:  92.00   3rd Qu.: 133.0      3rd Qu.: 351525   3rd Qu.:2566.5   3rd Qu.: 654.5   3rd Qu.:1858  
 Max.   : 1.29467   Max.   : 0.62020   Max.   :1973.0   Max.   :2456.00   Max.   :1556.0      Max.   :1425000   Max.   :6429.0   Max.   :3370.0   Max.   :4319  
 OtherEthnicGroup CentralHealingPercent   AvHholdSz       ComEstRes   
 Min.   :  16.0   Min.   :92.10         Min.   :1.600   Min.   :   0  
 1st Qu.: 134.0   1st Qu.:96.60         1st Qu.:2.300   1st Qu.:   9  
 Median : 232.0   Median :97.40         Median :2.500   Median :  41  
 Mean   : 285.8   Mean   :97.24         Mean   :2.506   Mean   : 102  
 3rd Qu.: 376.5   3rd Qu.:98.00         3rd Qu.:2.700   3rd Qu.: 105  
 Max.   :3001.0   Max.   :99.60         Max.   :3.900   Max.   :2172  

colSums(is.na(feature_df))
   RPDburglaryShifted     RPDRobberyShifted      total_burglaries       total_robberies   DwellingNoResidents      MedianHousePrice              FlatAprt 
                    0                     0                     0                     0                     0                     0                     0 
     fullTimeStudents                NoCars      OtherEthnicGroup CentralHealingPercent             AvHholdSz             ComEstRes 
                    0                     0                     0                     0                     0                     0 

As a quick initial exercise, we’ll create a scatter plot of the interaction between each and every one of our variables. This will probably be too messy to make any real findings, but can serve to quickly highlight strong associations.

pairs(feature_df)

As we hoped, some obvious relationships stand out: for instance, the presence of apartments, and households with no cars, or central heating and average household size.

Our robbery and burglary data and change rates are densely clustered - they’re unlikely to cleanly associate with anything. With that in mind, we’ll perform a log transformation. This cannot be undertaken with negative values, so once again we’ll perform a shift (of 2) for both of our relative error numbers, as well as a commercial resident column, before log transforming our features.

feature_df$BurglaryRPDTranform <- feature_df$RPDburglaryShifted    + 2
feature_df$RobberyRPDTranform <- feature_df$RPDRobberyShifted   + 2

feature_df$ComEstResTranform <- feature_df$ComEstRes   + 2
for (col in colnames(feature_df)){
  new_name <- paste("log_", col, sep = "")
  feature_df[new_name] <- log(feature_df[col])
}
NaNs producedNaNs produced

drop<- c( "log_ComEstRes", "log_RPDburglaryShifted", "log_RPDRobberyShifted")
feature_df<- feature_df[,!(names(feature_df) %in% drop)]

feat_transform_df <- feature_df[,17:29]
orig_feat_df <- feature_df[,0:17]


#feat_transform_df <- feature_df[,17:28]


colSums(is.na(feature_df))
       RPDburglaryShifted         RPDRobberyShifted          total_burglaries           total_robberies       DwellingNoResidents          MedianHousePrice 
                        0                         0                         0                         0                         0                         0 
                 FlatAprt          fullTimeStudents                    NoCars          OtherEthnicGroup     CentralHealingPercent                 AvHholdSz 
                        0                         0                         0                         0                         0                         0 
                ComEstRes       BurglaryRPDTranform        RobberyRPDTranform         ComEstResTranform      log_total_burglaries       log_total_robberies 
                        0                         0                         0                         0                         0                         0 
  log_DwellingNoResidents      log_MedianHousePrice              log_FlatAprt      log_fullTimeStudents                log_NoCars      log_OtherEthnicGroup 
                        0                         0                         0                         0                         0                         0 
log_CentralHealingPercent             log_AvHholdSz   log_BurglaryRPDTranform    log_RobberyRPDTranform     log_ComEstResTranform 
                        0                         0                         0                         0                         0 

We’ve now separated a separate dataframe where each value has been log transformed - while this isn’t hugely rigorous (and would benefit from inspecting the relationships in more detail) it serves our immediate purpose.

pairs(feat_transform_df)

While we’ve introduced a bit of noise, we’ve also “forced” some of our variables into relationships that look semi linear.

To dig into this deeper, let’s create a correlation matrix for our entire transformed dataframe.

correlate(feat_transform_df)

Correlation method: 'pearson'
Missing treated using: 'pairwise.complete.obs'

To provide a visual aid, I’ve extracted the column for our robbery relative change rate, and sorted the table accordingly.

dplyr::select(correlate(feat_transform_df)[order(correlate(feat_transform_df)$log_BurglaryRPDTranform),], term, log_BurglaryRPDTranform)

Correlation method: 'pearson'
Missing treated using: 'pairwise.complete.obs'


Correlation method: 'pearson'
Missing treated using: 'pairwise.complete.obs'

Regression

Now that we’ve transformed our data, cleaned it up, and identified potential correlates, let’s build our linear model.

There are various automated tools for this process that seek to provide the highest fit and significance, but given the high degree of correlation between my chosen features, I’ve taken a more manual approach and tested a variety of models until I identified one with a suitable fit. The final model is below.

mod_burglary <- lm(log_BurglaryRPDTranform ~ log_total_burglaries + log_FlatAprt + log_MedianHousePrice  + log_ComEstResTranform, data = feat_transform_df)
summary(mod_burglary)

Call:
lm(formula = log_BurglaryRPDTranform ~ log_total_burglaries + 
    log_FlatAprt + log_MedianHousePrice + log_ComEstResTranform, 
    data = feat_transform_df)

Residuals:
     Min       1Q   Median -0.06547 -0.00309  0.05830  0.56322 

Coefficients:
    
(Intercept)            1.255068   0.112681  11.138  -6.062 1.92e-09 ***
log_FlatAprt           0.016153   0.005157   3.132 0.001786 ***
log_ComEstResTranform -0.008125   0.002119  -3.833 0.000135 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.1027 on 974 degrees of freedom
Multiple R-squared: 
F-statistic: 21.72 974 DF,  p-value: < 2.2e-16

Our model suggests the largest burglary decrease linked to lockdown was in MSOAs which a high level of historic burglary. The composition of housing/accomodation and area type also seems to play a role, with those areas with higher median house prices, and a larger number of commercial residents, seeing stronger decreases, while conversely areas with large number of apartments temper the effect.

While all our variables are significant, the model is not a particularly good fit - the adjusted R2 is around 0.08, suggesting that less than 10% of the variance is accounted for by our model. I suspect more geographic features - such as distance from central London, more accurate footfall, or spatial lags - would probably be useful, but that’s outside the scope of this project.

Let’s perform a similar exercise for robbery.

dplyr::select(correlate(feat_transform_df)[order(correlate(feat_transform_df)$log_RobberyRPDTranform),], term, log_RobberyRPDTranform)

Correlation method: 'pearson'
Missing treated using: 'pairwise.complete.obs'


Correlation method: 'pearson'
Missing treated using: 'pairwise.complete.obs'
mod_burglary <- lm(log_RobberyRPDTranform ~ log_total_robberies  + log_total_burglaries + log_FlatAprt + log_CentralHealingPercent, data = feat_transform_df)
summary(mod_burglary)

Call:
lm(formula = log_RobberyRPDTranform ~ log_total_robberies + log_total_burglaries + 
    log_FlatAprt + log_CentralHealingPercent, data = feat_transform_df)

Residuals:
     Min       1Q   Median       3Q      Max 
-0.95347 -0.04269 -0.00516  0.04607  0.31963 

Coefficients:
                           Estimate Std. Error t value        Pr(>|t|)    
(Intercept)               -5.057332   1.394750  -3.626        0.000303 ***
log_total_robberies       -0.031452   0.004902  -6.416 0.0000000002177 ***
log_total_burglaries      -0.066422   0.009692  -6.853 0.0000000000128 ***
log_FlatAprt               0.029271   0.005070   5.773 0.0000000104411 ***
log_CentralHealingPercent  1.304434   0.301621   4.325 0.0000168425948 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.08917 on 974 degrees of freedom
Multiple R-squared:  0.21020.207 
F-statistic: 64.81 on 4 and 974 DF,  p-value: < 0.00000000000000022

This is a notably better fit than our burglary model, with our R2 suggesting we now account for over 20% of the variance. The nature of our predictors is also quite different: while we still see a negative relationship with historic crime (with areas of high historic crime experiencing larger relative decreases), there is a positive relationship with both the presence of apartments and central heating.

I suspect some of these features are correlates of deprivation, so I want to create a quick scatter of three - for now we’ll do it against median house price, which is definitely deprivation correlated.


heating <- ggplot(feature_df, aes(x = log_MedianHousePrice, y = log_CentralHealingPercent)) +
  geom_point()+
  geom_smooth(method=lm)

apartments <- ggplot(feature_df, aes(x = log_MedianHousePrice, y = log_FlatAprt)) +
  geom_smooth(method=lm)

comest <- ggplot(feature_df, aes(x = log_MedianHousePrice, y = log_ComEstResTranform)) +
  geom_point()+
  geom_smooth(method=lm)
`geom_smooth()` using formula 'y ~ x'
`geom_smooth()` using formula 'y ~ x'

While there does appear to be a relationship with some of these, it isn’t strong - this suggests the factor’s we have identified are significant not because of their association with deprivation and poverty, but because of what they mean about the specific characteristics of the area.

Random Forests

Unlike regression, random forest doesn’t really on any specific type of association - instead, we rely on computing power, repetition and iteration to capture the very best predictor for our variable, in any combination.

There are risks to this method: our sample size is smaller than I’d like, and this may lead to over-fit of outlier MSOAs.

It does mean we don’t need to worry about transformations or correlations: we can return to our original dataset, and let the model identify the strongest predictors.

# we remove rows where our main error is na or missing
rf_msoa_matrix <- drop_na(msoa_matrix_numeric, RPDRobberyShifted)
clean_rf_matrix <- rf_msoa_matrix[ , colSums(is.na(rf_msoa_matrix)) == 0]

#then we drop out any values that directly predict our error.

drop<- c("burglaryActual","burglaryError","burglaryPercentError","burglaryPredicted","robberyActual","robberyPredicted","robberyError","robberyPercentError", "RPDBurglaryShifted", "RPDRobberyShifted")

#remove out selected columns
data<- clean_rf_matrix[,!(names(clean_rf_matrix) %in% drop)]


names(clean_rf_matrix)<-make.names(names(clean_rf_matrix),unique = TRUE)

drop<- c("burglaryActual","burglaryError","robberyActual","robberyError","RPDBurglary","RPDRobbery","robberyActualShifted","robberyPredictedShifted","burglaryActualShifted","burglaryPredictedShifted", "burglaryPredicted", "burglaryPercentError", "robberyPredicted", "robberyPercentError")
#drop<- c("burglaryPercentError","burglaryPredicted","robberyPredicted","robberyPercentError")

We start with modelling our relative rate of burglary shift. We divide our sample into a training set which we’ll use to train the model, and a test set we’ll use to verify accuracy and validity.

sample = sample.split(data$RPDburglaryShifted, SplitRatio = 0.7)
train = subset(data, sample == TRUE)
test  = subset(data, sample == FALSE)

  RPDburglaryShifted ~ .,
  data=train, 

summary(rf_burglary)
                Length Class  Mode     
call              1    -none- -none- numeric  
mse            
rsq             500    -none- numeric  
oob.times       685    -none- numeric   -none- numeric  
localImportance   0    -none- NULL     
ntree             1    numeric  
forest           11    -none- list     
coefs             0    -none- NULL     
y               685      0    -none- NULL     
terms             3   
prediction <-predict(rf_burglary, test)
Metrics::rmse(test$RPDburglaryShifted, prediction)
[1] 0.2086745

While machine learning models were once considered opaque and difficult to interpret, several libraries now offer functionality to explain predictions. Here I use DALEX to do just this.


rf_explainer_burglary <- DALEX::explain(rf_burglary, data=train, y= train$RPDburglaryShifted)
Preparation of a new explainer is initiated
  -> model label       :   (  default )
  -> data              :  685  rows  211  cols 
  -> data              :  tibble converted into a data.frame 
  -> target variable   :    -> predict function  :  yhat.randomForest  will be used (  default  )
  -> predicted values  :  No value for predict function target column. (  default  )
 randomForest , ver. 4.6.14 , taskdefault  ) 
  -> predicted values  :  numerical, min =  -0.5780085 , mean =  -0.08106178 , max =  0.3933345  
  -> residual function :  difference between y and yhat (  default  )
  -> residuals         :  numerical, min =  -0.2656502 , mean =  -0.000773038 , max =  0.3310273  
  A new explainer has been created! 
rf_perf_burg
 
rmse       : 0.07978734 
r2         : 0.8458048 
mad        : 0.04547341

Residuals:
          0%          10%          20%          30%          40%          50%          60%          70%          80%          90%         100% 
-0.265650178 -0.088750799 -0.057666182 -0.039718463 -0.023652909 -0.007873967  0.008104222  0.029419548  0.052525556  0.089675687  0.331027295 

We can see that our model significantly outperforms our best linear models: the R2 suggests that almost 85% of the variance is correctly interpreted, and our rmse (root mean squared error) is around 0.2 on our test set.

This model would be ill-suited to prediction or operationalising -it is a default forecast with no hyper-parameter tuning, and no consideration of error rates - but using tools like DALEX, we can identify which predictors the model identifies as most important.

model_parts_burg <-model_parts(rf_explainer_burglary)
model_parts_burg
                                                                                                      variable mean_dropout_loss        label
1                                                                                           RPDburglaryShifted        0.07978734 randomForest
3                                                                                   Road.Casualties.2010.Fatal        0.07989223 randomForest
4                                                                                   Road.Casualties.2011.Fatal        0.07990359 randomForest
5                                                                                   Road.Casualties.2012.Fatal        0.07994289 randomForest
6                                                                         Age.Structure..2011.Census..All.Ages        0.08016856 randomForest
7                                                                       Mid.year.Estimate.totals.All.Ages.2010        0.08020098 randomForest
8                                Car.or.van.availability..2011.Census..4.or.more.cars.or.vans.in.household....        0.08023165 randomForest
9                                                                                                     UsualRes        0.08027333 randomForest
10  randomForest
12                                                                            Households..2011..All.Households        0.08034082 randomForest
13                                                                      Mid.year.Estimate.totals.All.Ages.2011        0.08034805 randomForest
14                                                                        Ethnic.Group..2011.Census..White....        0.08035199 randomForest
15                                                                      Mid.year.Estimate.totals.All.Ages.2012        0.08035832 randomForest
16                                                                                                    HholdRes        0.08036393 randomForest
17                           Qualifications..2011.Census..Highest.level.of.qualification..Other.qualifications        0.08036488 randomForest
18  randomForest
20                                           Car.or.van.availability..2011.Census..2.cars.or.vans.in.household
22                                                              Country.of.Birth..2011..Not.United.Kingdom....        0.08044878 randomForest                                                                     Mid.year.Estimate.totals.All.Ages.2006        0.08047061 randomForest
25                                                                     Tenure..2011..Owned..Owned.outright....        0.08047637 randomForest
26                                                                         Ethnic.Group..2011.Census..BAME....        0.08047866 randomForest
27                                                                             Ethnic.Group..2011.Census..BAME        0.08049934 randomForest
28                                                                          Religion..2011..Other.religion....        0.08050526 randomForest
29                                      Dwelling.type..2011..Household.spaces.with.at.least.one.usual.resident        0.08053065 randomForest
30                                                                                                      Hholds        0.08054706 randomForest
31  Household.Language..2011..At.least.one.person.aged.16.and.over.in.household.has.English.as.a.main.language        0.08057152 randomForest
32                                                 Health..2011.Census..Day.to.day.activities.limited.a.little        0.08059003 randomForest
33                                                                                    Religion..2011..Sikh....        0.08059177 randomForest
34                                                               Population.Density.Persons.per.hectare..2012.        0.08059472 randomForest
35      Household.Language..2011....of.households.where.no.people.in.household.have.English.as.a.main.language        0.08060243 randomForest
36                                                                                Road.Casualties.2011.Serious        0.08060476 randomForest
37                            Household.Language..2011..No.people.in.household.have.English.as.a.main.language        0.08060958 randomForest
38                                   Car.or.van.availability..2011.Census..Sum.of.all.cars.or.vans.in.the.area        0.08064046 randomForest
39                                                                  Country.of.Birth..2011..Not.United.Kingdom        0.08066560 randomForest
42                                                                           Age.Structure..2011.Census..30.44        0.08066940 randomForest
43                         Qualifications..2011.Census..Highest.level.of.qualification..Level.1.qualifications        0.08067143 randomForest
44                                       Car.or.van.availability..2011.Census..3.cars.or.vans.in.household....        0.08067284 randomForest
45                                                          Tenure..2011..Owned..Owned.with.a.mortgage.or.loan        0.08067322 randomForest
46                                                                  Country.of.Birth..2011..United.Kingdom....        0.08068890 randomForest
47                                                  Economic.Activity..2011.Census..Economically.active..Total        0.08069008 randomForest
48                                                                      Mid.year.Estimate.totals.All.Ages.2004        0.08069682 randomForest
49                                                                      Country.of.Birth..2011..United.Kingdom        0.08071084 randomForest
50                                                                      Mid.year.Estimate.totals.All.Ages.2003        0.08071974 randomForest
51                                Lone.Parents..2011.Census..All.lone.parent.housholds.with.dependent.children        0.08073043 randomForest
52                                             Health..2011.Census..Day.to.day.activities.limited.a.little....        0.08075471 randomForest
55                                                                             Tenure..2011..Social.rented....        0.08076387 randomForest
56                                                                                                      PopDen        0.08076430 randomForest
57                                                                       Mid.year.Estimates.2012..by.age.60.64        0.08077331 randomForest
58                                                                      Mid.year.Estimate.totals.All.Ages.2008        0.08077994 randomForest
59                                                                             Religion..2011..No.religion....        0.08078100 randomForest
60                                                                                     House.Prices.Sales.2010        0.08078206 randomForest
61                                                                      Mid.year.Estimate.totals.All.Ages.2009        0.08078457 randomForest
62                                                     Economic.Activity..2011.Census..Economically.inactive..        0.08079916 randomForest
63                                                              Ethnic.Group..2011.Census..Asian.Asian.British        0.08080477 randomForest
64                                           Car.or.van.availability..2011.Census..3.cars.or.vans.in.household        0.08080990 randomForest
65                                                                       Mid.year.Estimates.2012..by.age.85.89        0.08081135 randomForest
66                                                      Tenure..2011..Owned..Owned.with.a.mortgage.or.loan....        0.08082316 randomForest
67                                                                           Age.Structure..2011.Census..16.29        0.08083177 randomForest
68               Qualifications..2011.Census..Highest.level.of.qualification..Level.4.qualifications.and.above        0.08083667 randomForest
69                                                                           Age.Structure..2011.Census..45.64        0.08083957 randomForest
70                                                                       Mid.year.Estimates.2012..by.age.55.59        0.08084109 randomForest
71                                                       Economic.Activity..2011.Census..Economically.active..        0.08084118 randomForest
72                                                                                Religion..2011..Buddhist....        0.08084915 randomForest
73                                                                    House.Prices.Median.House.Price.....2011        0.08085332 randomForest
74                                                                                   Religion..2011..Hindu....        0.08085661 randomForest
75                                           Central.Heating..2011.Census..Households.with.central.heating....        0.08085781 randomForest
76                         Qualifications..2011.Census..Highest.level.of.qualification..Level.2.qualifications        0.08086017 randomForest
77                                                               Ethnic.Group..2011.Census..Other.ethnic.group        0.08086059 randomForest
78                                             Economic.Activity..2011.Census..Economically.active..Unemployed        0.08086791 randomForest
79                                                                                  Religion..2011..Jewish....        0.08087423 randomForest
80                                             Dwelling.type..2011..Whole.house.or.bungalow..Semi.detached....        0.08087529 randomForest
81                                                   Household.Composition..2011..Numbers.One.person.household        0.08087823 randomForest
82                                                                       Mid.year.Estimates.2012..by.age.80.84        0.08088729 randomForest
83                                                  Household.Composition..2011..Numbers.Lone.parent.household        0.08088891 randomForest        0.08092207
87                            Household.Composition..2011..Numbers.Couple.household.without.dependent.children        0.08093548 randomForest
88            Adults.in.Employment..2011.Census..No.adults.in.employment.in.household..With.dependent.children        0.08093596 randomForest
89                                                                    House.Prices.Median.House.Price.....2005        0.08094486 randomForest
90                                                                      Mid.year.Estimate.totals.All.Ages.2002        0.08094711 randomForest
91            Income.Deprivation..2010....living.in.income.deprived.households.reliant.on.means.tested.benefit        0.08094734 randomForest
92                                                Economic.Activity..2011.Census..Economically.inactive..Total        0.08095970 randomForest
93                                                          Dwelling.type..2011..Flat..maisonette.or.apartment        0.08097084 randomForest
94    Adults.in.Employment..2011.Census....of.households.with.no.adults.in.employment..With.dependent.children        0.08097164 randomForest
95                                                                       Mid.year.Estimates.2012..by.age.15.19        0.08097487 randomForest
96                                 Qualifications..2011.Census..Highest.level.of.qualification..Apprenticeship        0.08099627 randomForest
97                                                                                Road.Casualties.2010.Serious        0.08099896 randomForest
98 
100                                         Car.or.van.availability..2011.Census..No.cars.or.vans.in.household        0.08100307 randomForest
101                        Qualifications..2011.Census..Schoolchildren.and.full.time.students..Age.18.and.over        0.08102459 randomForest
102                                                                   House.Prices.Median.House.Price.....2006        0.08102808 randomForest
103                                        Car.or.van.availability..2011.Census..1.car.or.van.in.household....        0.08102910 randomForest
104                                                                              House.Prices.Sales.2011...130        0.08103290 randomForest
105                                                                   House.Prices.Median.House.Price.....2010        0.08103351 randomForest
106                                                                                Religion..2011..No.religion        0.08104129 randomForest
107                                                                                 Religion..2011..Muslim....        0.08104171 randomForest
108 randomForest
110                                                Dwelling.type..2011..Whole.house.or.bungalow..Semi.detached        0.08107212 randomForest
111                                                                               Tenure..2011..Private.rented        0.08107812 randomForest
112                              Household.Composition..2011..Numbers.Couple.household.with.dependent.children randomForest
114                                                     Dwelling.type..2011..Flat..maisonette.or.apartment....        0.08110023 randomForest
117                                                                        Mid.year.Estimates.2012..by.age.90.        0.08110115 randomForest
118                                                                   House.Prices.Median.House.Price.....2009        0.08112692 randomForest
119                                                                                 House.Prices.Sales.2013.p.        0.08112842 randomForest
120                                                                                Tenure..2011..Social.rented        0.08113023 randomForest
121                                                                        Mid.year.Estimates.2012..by.age.5.9        0.08113618 randomForest
122                                                                   House.Prices.Median.House.Price.....2008        0.08114446 randomForest
123                                                 Household.Composition..2011..Numbers.Other.household.Types        0.08116352 randomForest
124              Obesity.Percentage.of.the.population.aged.16..with.a.BMI.of.30...modelled.estimate..2006.2008        0.08116727 randomForest
125                                            Car.or.van.availability..2011.Census..1.car.or.van.in.household        0.08116794 randomForest
126                                                                  Health..2011.Census..Very.good.health....        0.08118887 randomForest
127                                                                      Mid.year.Estimates.2012..by.age.25.29        0.08120511 randomForest
128                                                                                      Religion..2011..Hindu        0.08122569 randomForest
129                                                                            Health..2011.Census..Bad.health        0.08123266 randomForest
130                                                                      Mid.year.Estimates.2012..by.age...65.        0.08123475 randomForest
131                                                                                         Land.Area.Hectares        0.08124618 randomForest
132                                                         Ethnic.Group..2011.Census..Asian.Asian.British....        0.08125689 randomForest
133                                                                                    House.Prices.Sales.2009        0.08127707 randomForest
134                                                             Qualifications..2011.Census..No.qualifications        0.08128507 randomForest
135                                                                      Mid.year.Estimates.2012..by.age.30.34        0.08131069 randomForest
136                                       Ethnic.Group..2011.Census..Black.African.Caribbean.Black.British....        0.08131640 randomForest
137                                                                            Age.Structure..2011.Census..65.        0.08131793 randomForest
138                                                                      Mid.year.Estimates.2012..by.age.75.79        0.08132623 randomForest
139                                           Ethnic.Group..2011.Census..Black.African.Caribbean.Black.British        0.08132628 randomForest
140                                                                           Ethnic.Group..2011.Census..White        0.08133305 randomForest
141                                                                      Mid.year.Estimates.2012..by.age.50.54        0.08134709 randomForest        0.08136569        0.08136868 randomForest
146 randomForest
148                                                                   House.Prices.Median.House.Price.....2012        0.08141885 randomForest
149                                                                       Health..2011.Census..Fair.health....        0.08142456 randomForest
150                                                                                                  AvHholdSz        0.08142887 randomForest
151                                                                                      Life.Expectancy.Males        0.08143464 randomForest
152                                                                    Religion..2011..Religion.not.stated....        0.08144721 randomForest
153                                                                                   Religion..2011..Buddhist        0.08146208 randomForest
154                                           Low.Birth.Weight.Births..2007.2011..LCL...Lower.confidence.limit        0.08146848 randomForest
155                                                                                       Religion..2011..Sikh        0.08149141 randomForest
156                                                                      Health..2011.Census..Very.good.health        0.08149203 randomForest
157                                            Low.Birth.Weight.Births..2007.2011..Low.Birth.Weight.Births....        0.08149302 randomForest
158                                                                      Mid.year.Estimates.2012..by.age.35.39        0.08149439 randomForest
159                                                   Health..2011.Census..Day.to.day.activities.limited.a.lot        0.08149561 randomForest
160                                                                        Tenure..2011..Owned..Owned.outright        0.08149998 randomForest
161                                                                                Road.Casualties.2010.Slight        0.08150819 randomForest
162                                           Low.Birth.Weight.Births..2007.2011..UCL...Upper.confidence.limit        0.08151073 randomForest
163                                                                               Road.Casualties.2012.Serious        0.08153523 randomForest
164                                                                           Tenure..2011..Private.rented....        0.08154695 randomForest
165                                                                                    House.Prices.Sales.2007        0.08156845 randomForest
166                                                 Health..2011.Census..Day.to.day.activities.not.limited....        0.08164471 randomForest
167                                                                            Road.Casualties.2012.2012.Total        0.08166058 randomForest
168                                                                            Road.Casualties.2010.2010.Total        0.08167894 randomForest
169                                                                             Religion..2011..Other.religion        0.08168736 randomForest
170                                                                                Road.Casualties.2012.Slight        0.08169606 randomForest
171                                                                      Mid.year.Estimates.2012..by.age.40.44        0.08173699 randomForest
172                                                                     Mid.year.Estimate.totals.All.Ages.2007        0.08173808 randomForest
173                                               Health..2011.Census..Day.to.day.activities.limited.a.lot....        0.08174045 randomForest
174                                                    Ethnic.Group..2011.Census..Mixed.multiple.ethnic.groups randomForest
177                        Qualifications..2011.Census..Highest.level.of.qualification..Level.3.qualifications        0.08175634 randomForest
178                                                     Dwelling.type..2011..Whole.house.or.bungalow..Detached        0.08177575 randomForest
179                                                                                  Religion..2011..Christian        0.08179686 randomForest
180                                                                                    House.Prices.Sales.2005        0.08182753 randomForest
181                                                                   House.Prices.Median.House.Price.....2007        0.08184118 randomForest
182                                                                        Health..2011.Census..Bad.health....        0.08185248 randomForest
183                                                                       Health..2011.Census..Good.health....        0.08194459 randomForest
184                                                                                            total_robberies        0.08196227 randomForest
185                                                                                    House.Prices.Sales.2006        0.08196583 randomForest
186                                          Dwelling.type..2011..Household.spaces.with.no.usual.residents....        0.08200226 randomForest
187                                                                            Road.Casualties.2011.2011.Total        0.08203031 randomForest
188                             Dwelling.type..2011..Whole.house.or.bungalow..Terraced..including.end.terrace.        0.08204300 randomForest
189                                                                      Mid.year.Estimates.2012..by.age.20.24        0.08210720 randomForest
190                                                                      Mid.year.Estimates.2012..by.age.65.69        0.08211403 randomForest
191                                                 Dwelling.type..2011..Whole.house.or.bungalow..Detached....        0.08213368 randomForest
192                                Household.Income.Estimates..2011.12..Total.Mean.Annual.Household.Income....        0.08215211 randomForest
193                                                                      Mid.year.Estimates.2012..by.age.70.74        0.08221997 randomForest
194                                                                          Incidence.of.Cancer.Breast.Cancer        0.08229737 randomForest
195                                                                                Road.Casualties.2011.Slight        0.08231561 randomForest
196                                                          Economic.Activity..2011.Census..Unemployment.Rate        0.08239690 randomForest
197                                                 Lone.Parents..2011.Census..Lone.parent.not.in.employment..        0.08246826 randomForest
198        0.08262825 randomForest
200                                              Dwelling.type..2011..Household.spaces.with.no.usual.residents        0.08264973 randomForest
201                                                                                    Life.Expectancy.Females        0.08276533 randomForest
202                         Dwelling.type..2011..Whole.house.or.bungalow..Terraced..including.end.terrace.....        0.08284255 randomForest
203                                                                                     Religion..2011..Jewish        0.08293921 randomForest
204                                                                                    Incidence.of.Cancer.All        0.08306588 randomForest
205                                                                                          RPDRobberyShifted        0.08370759 randomForest
206                          Household.Composition..2011..Percentages.Couple.household.with.dependent.children        0.08393367 randomForest
207                                                                                    House.Prices.Sales.2008        0.08433984 randomForest
208                       Household.Composition..2011..Percentages.Couple.household.without.dependent.children        0.08459338 randomForest
209                                                                  Mid.year.Estimates.2012..by.age...0.to.14        0.08578863 randomForest
210                                                                                           total_burglaries        0.08833999 randomForest
211                                                                                                  ComEstRes        0.09121371 randomForest
212                                                                        Mid.year.Estimates.2012..by.age.0.4        0.09159861 randomForest
213                                                                                                 _baseline_        0.24106307 randomForest
plot(model_parts_burg, max_vars=25)

The three most important features our model highlights are: - the age composition of the population - the number of residents which are in commercial property - the historic number of burglaries

This seems to corroborate our previous regression model. To further unpick these trends, we can use Partial Dependence Plots to identify how the model prediction shifts with these values.

pdp <- model_profile(rf_explainer_burglary)
plot(pdp, variables="total_burglaries")

We still see a strong association between a high number of historic, and a large reduction during the lockdown period

plot(pdp, variables= "Mid.year.Estimates.2012..by.age.0.4")

MSOAs with very large very young populations seem to have a less strong burglary lockdown decrease (though this is likely heavily associated to deprivation)

plot(pdp, variables="ComEstRes")

hist(msoa_matrix_numeric$ComEstRes)

By combining the distribution of commercial residents by MSOA with our PDP, we can see that those MSOAs that are most densely populated by commercial residents see the smallest “covid decrease”(suggesting that those MSOAs that are very heavily residential saw the sharpest drops).

plot(pdp, variables="House.Prices.Sales.2008")

Finally, we can see that those areas that experienced the highest volume of house sales experienced the lowest relative decrease in burglary.

This highlights the importance of identifying correlates in RF models - especially in a dataset where features are highly interlinked, association does not imply causation, and we should be wary of over-interpreting.

We can now repeat our process for our robbery shift.


sample = sample.split(data$RPDRobberyShifted, SplitRatio = 0.75)
train = subset(data, sample == TRUE)
test  = subset(data, sample == FALSE)


rf_robbery <- randomForest(
  RPDRobberyShifted ~ .,
  data=train, 
  importance=TRUE
)

summary(rf_robbery)
 Length Class  Mode     
call            -none- character
predicted       734    -none- numeric  
rsq             500    -none- numeric  
importance      420    -none- numeric  
localImportance   0      0    -none- NULL     
ntree             1    -none- numeric  
mtry              1    -none- numeric  
forest           11    -none- list     
coefs             0    -none- NULL     
y               734    -none- numeric  
test              0    -none- NULL     
inbag             0    -none- NULL     
terms             3    terms  call     

We’ve now trained a model. Let’s now use the DALEX library to understand it, and see how it performs.


rf_explainer_robbery <- DALEX::explain(rf_robbery, data=train, y= train$RPDRobberyShifted)
Preparation of a new explainer is initiated
  -> model label       :  randomForest  (  default  )
  -> data              :  734  rows  211  cols 
  -> data              :  tibble converted into a data.frame 
  -> target variable   :  734  values 
 yhat.randomForest  will be used (  default  )
  -> predicted values  :  No value for predict function target column. (  default  )
 4.6.14 , task regression (  ) 
  -> predicted values  :  numerical, min =  -0.9645244 , mean =  -0.0470117 , max =  0.3797893  
  -> residual function :  difference between y and yhat (  default  )
  -> residuals         :  numerical, min =  -0.4903862 , mean =  -0.001156124 , max =  0.2960573  
 
rf_perf_rob <- model_performance(rf_explainer_robbery)
rf_perf_rob
Measures for:  
r2         : 0.8666274 
mad        : 0.02860048

Residuals:
          0%          10%          20%          30%          40%          50%          60%          70%          80%          90%         100% 
-0.490386240 -0.062713767 -0.038399387 -0.024521257 -0.013158676 -0.004124880  0.004984989  0.019451443  0.035391571  0.063885825  0.296057263 
model_parts_rob <-model_parts(rf_explainer_robbery)
model_parts_rob
                                                                                                      variable mean_dropout_loss        label
1                                                                                                 _full_model_        0.05952187 randomForest
2                                                                                            RPDRobberyShifted        0.05952187 randomForest
3                                                                                   Road.Casualties.2012.Fatal        0.05956864 randomForest
4                                                                                   Road.Casualties.2010.Fatal        0.05958931 randomForest
5                                                                                   Road.Casualties.2011.Fatal        0.05959538 randomForest
6                                                                                                     HholdRes        0.05970861 randomForest
7                                                                       Mid.year.Estimate.totals.All.Ages.2010        0.05973753 randomForest
8                                Car.or.van.availability..2011.Census..4.or.more.cars.or.vans.in.household....        0.05975769 randomForest
9                                                                       Mid.year.Estimate.totals.All.Ages.2011        0.05976137 randomForest
10                                                      Health..2011.Census..Day.to.day.activities.not.limited        0.05977415 randomForest
11                                                                                                   AvHholdSz        0.05977911 randomForest
12                                                                        Age.Structure..2011.Census..All.Ages        0.05978227 randomForest
13                                                                                                    UsualRes        0.05979675 randomForest
14                                Lone.Parents..2011.Census..All.lone.parent.housholds.with.dependent.children        0.05980643 randomForest
15                                                                      Mid.year.Estimate.totals.All.Ages.2006        0.05981345 randomForest
16                                           Car.or.van.availability..2011.Census..2.cars.or.vans.in.household        0.05986355 randomForest
17                                      Dwelling.type..2011..Household.spaces.with.at.least.one.usual.resident        0.05986499 randomForest
18                                                                         Tenure..2011..Owned..Owned.outright        0.05986769 randomForest        0.05988390 randomForest        0.05988822 randomForest
23                                                                                Road.Casualties.2010.Serious        0.05988899 randomForest
24    Adults.in.Employment..2011.Census....of.households.with.no.adults.in.employment..With.dependent.children        0.05988994 randomForest
25                                                                    House.Prices.Median.House.Price.....2009        0.05989951 randomForest
26                                                  Economic.Activity..2011.Census..Economically.active..Total        0.05990367 randomForest
27                                                                                  Religion..2011..Jewish....        0.05991359 randomForest
28  Household.Language..2011..At.least.one.person.aged.16.and.over.in.household.has.English.as.a.main.language        0.05991422 randomForest
29                                                  Dwelling.type..2011..Whole.house.or.bungalow..Detached....        0.05991695 randomForest
30                                                      Dwelling.type..2011..Whole.house.or.bungalow..Detached        0.05991703 randomForest
31                                             Dwelling.type..2011..Whole.house.or.bungalow..Semi.detached....        0.05992179 randomForest
32                                                                    House.Prices.Median.House.Price.....2010        0.05992630 randomForest
33                                                                       Mid.year.Estimates.2012..by.age.70.74        0.05993161 randomForest
34                                   Car.or.van.availability..2011.Census..4.or.more.cars.or.vans.in.household        0.05993504 randomForest
35  randomForest
37                                                                      Mid.year.Estimate.totals.All.Ages.2007        0.05995053 randomForest
38                                                                      Mid.year.Estimate.totals.All.Ages.2004        0.05996353 randomForest
39                                                                      Mid.year.Estimate.totals.All.Ages.2012        0.05996873 randomForest
40                                                 Dwelling.type..2011..Whole.house.or.bungalow..Semi.detached        0.05997034 randomForest
41                                                                             Age.Structure..2011.Census..65.        0.05997184 randomForest
42                         Qualifications..2011.Census..Highest.level.of.qualification..Level.2.qualifications        0.05997500 randomForest
43                                                                          Religion..2011..Other.religion....        0.05997794 randomForest
44                                                                       Health..2011.Census..Very.good.health        0.05997835 randomForest
45                                                                    House.Prices.Median.House.Price.....2005        0.05998924 randomForest
46                                                                             Tenure..2011..Social.rented....        0.05999127 randomForest
47                                                                     Age.Structure..2011.Census..Working.age        0.05999621 randomForest
48                                                                       Mid.year.Estimates.2012..by.age...65.        0.06001570 randomForest
49                                           Car.or.van.availability..2011.Census..3.cars.or.vans.in.household
52                                                                    House.Prices.Median.House.Price.....2011        0.06004060 randomForest
53                                                  Household.Composition..2011..Numbers.Lone.parent.household        0.06004582 randomForest
54               Obesity.Percentage.of.the.population.aged.16..with.a.BMI.of.30...modelled.estimate..2006.2008        0.06004786 randomForest
55                                   Car.or.van.availability..2011.Census..Sum.of.all.cars.or.vans.in.the.area        0.06004791 randomForest
56                                                                       Mid.year.Estimates.2012..by.age.80.84        0.06004946 randomForest
57                                                                       Mid.year.Estimates.2012..by.age.50.54        0.06005044 randomForest        0.06005591 randomForest
60                                                                           Age.Structure..2011.Census..30.44        0.06005931 randomForest
61                                             Car.or.van.availability..2011.Census..1.car.or.van.in.household        0.06006814 randomForest
62            Adults.in.Employment..2011.Census..No.adults.in.employment.in.household..With.dependent.children        0.06007092 randomForest
63                                                                            Households..2011..All.Households        0.06007556 randomForest
64                                                                    House.Prices.Median.House.Price.....2007        0.06007826 randomForest
65                                                     Economic.Activity..2011.Census..Economically.inactive..        0.06008955 randomForest
66                                 Household.Income.Estimates..2011.12..Total.Mean.Annual.Household.Income....        0.06009647 randomForest randomForest
69                                                              Qualifications..2011.Census..No.qualifications        0.06010873 randomForest
70                                                   Lone.Parents..2011.Census..Lone.parents.not.in.employment        0.06011036 randomForest
71                                                                            Age.Structure..2011.Census..0.15        0.06011788 randomForest
72                                              Household.Composition..2011..Percentages.Lone.parent.household        0.06011867 randomForest
73                                                                       Mid.year.Estimates.2012..by.age.40.44        0.06012597 randomForest
74                                                                               House.Prices.Sales.2011...129        0.06012701 randomForest
75            Income.Deprivation..2010....living.in.income.deprived.households.reliant.on.means.tested.benefit        0.06012765 randomForest
76                                                                         Health..2011.Census..Bad.health....        0.06013151 randomForest
77                                                                House.Prices.Median.House.Price.....2013..p.        0.06013614        0.06016171 randomForest
80                                                                      Country.of.Birth..2011..United.Kingdom        0.06016239 randomForest
81                                                                                  House.Prices.Sales.2013.p.        0.06016255 randomForest        0.06017141 randomForest
84                                                           Economic.Activity..2011.Census..Unemployment.Rate        0.06017764 randomForest
85                        Household.Composition..2011..Percentages.Couple.household.without.dependent.children        0.06019165 randomForest
86                                                                                     House.Prices.Sales.2010        0.06019170 randomForest
87                                                                                     House.Prices.Sales.2005        0.06019370 randomForest
88                                                                                     House.Prices.Sales.2006        0.06019433 randomForest
89                                                                       Mid.year.Estimates.2012..by.age.55.59        0.06019794 randomForest
90                                             Health..2011.Census..Day.to.day.activities.limited.a.little....        0.06019800 randomForest
91                                                       Economic.Activity..2011.Census..Economically.active..        0.06020157 randomForest
92                                                                     Tenure..2011..Owned..Owned.outright....        0.06020697 randomForest
93                                                                       Mid.year.Estimates.2012..by.age.30.34        0.06020928 randomForest
94                                                                    House.Prices.Median.House.Price.....2012        0.06020958 randomForest
95                                                                       Mid.year.Estimates.2012..by.age.45.49        0.06022425 randomForest
96                                           Central.Heating..2011.Census..Households.with.central.heating....        0.06023901 randomForest
97                                                                                      Religion..2011..Jewish        0.06024087 randomForest
98                                                                    Health..2011.Census..Very.bad.health....        0.06024264 randomForest
99                               Household.Composition..2011..Numbers.Couple.household.with.dependent.children        0.06025090 randomForest
100                                                                      Mid.year.Estimates.2012..by.age.75.79        0.06025885 randomForest
101                                                                     Mid.year.Estimate.totals.All.Ages.2002        0.06027020 randomForest
102                              Household.Income.Estimates..2011.12..Total.Median.Annual.Household.Income....        0.06027310 randomForest
103                           Household.Composition..2011..Numbers.Couple.household.without.dependent.children        0.06027733 randomForest
104                        Qualifications..2011.Census..Highest.level.of.qualification..Level.1.qualifications        0.06027961 randomForest
105                                 Dwelling.type..2011..Household.spaces.with.at.least.one.usual.resident....        0.06029249 randomForest
106                                                     Tenure..2011..Owned..Owned.with.a.mortgage.or.loan....        0.06029446 randomForest
107                                              Dwelling.type..2011..Household.spaces.with.no.usual.residents        0.06031695 randomForest
108                                                                                Religion..2011..No.religion        0.06031908 randomForest
109 randomForest        0.06032636 randomForest
113                                               Health..2011.Census..Day.to.day.activities.limited.a.lot....        0.06032787 randomForest
114                                                                        Mid.year.Estimates.2012..by.age.5.9        0.06032920 randomForest
115                                                                               Road.Casualties.2012.Serious        0.06033966 randomForest
116                                                                           Health..2011.Census..Good.health        0.06034929 randomForest
117                                                                            Religion..2011..No.religion....        0.06036163 randomForest
118                   Income.Deprivation..2010....of.people.aged.over.60.who.live.in.pension.credit.households        0.06036686 randomForest
119                                                                                  Religion..2011..Hindu....        0.06036907 randomForest
120                                                         Dwelling.type..2011..Flat..maisonette.or.apartment        0.06037343 randomForest
121                                                                       Health..2011.Census..Fair.health....        0.06037424 randomForest
122                             Dwelling.type..2011..Whole.house.or.bungalow..Terraced..including.end.terrace.        0.06037583 randomForest
123                                                 Lone.Parents..2011.Census..Lone.parent.not.in.employment..        0.06037930        0.06038862 randomForest
126                                            Economic.Activity..2011.Census..Economically.active..Unemployed        0.06039167 randomForest
127                                                                   House.Prices.Median.House.Price.....2008        0.06039358 randomForest
128                                                                              Religion..2011..Christian....        0.06039596 randomForest
129                                                                      Mid.year.Estimates.2012..by.age.20.24        0.06039727 randomForest
130                                                                             Religion..2011..Other.religion        0.06039886 randomForest
131                                                                                                  ComEstRes        0.06040057 randomForest
132                                             Household.Composition..2011..Percentages.Other.household.Types        0.06040106 randomForest
133                                                                                    House.Prices.Sales.2007
135                                                 Household.Composition..2011..Numbers.Other.household.Types        0.06040495 randomForest
138                                          Dwelling.type..2011..Household.spaces.with.no.usual.residents....        0.06044575 randomForest
139                                                                                 Religion..2011..Muslim....        0.06045004 randomForest
140                                                Health..2011.Census..Day.to.day.activities.limited.a.little        0.06045210 randomForest
141                                                                           Tenure..2011..Private.rented....        0.06045264 randomForest
142                                                                           Ethnic.Group..2011.Census..White        0.06045855                                           Low.Birth.Weight.Births..2007.2011..LCL...Lower.confidence.limit        0.06046500 randomForest
145                                                     Dwelling.type..2011..Flat..maisonette.or.apartment....        0.06046511 randomForest
146                                                                                    House.Prices.Sales.2008        0.06046573 randomForest
147                                                                                  Religion..2011..Christian        0.06046620 randomForest
148                                      Car.or.van.availability..2011.Census..2.cars.or.vans.in.household....        0.06046913 randomForest
149                                                             Ethnic.Group..2011.Census..Asian.Asian.British        0.06048039 randomForest
150                                                                                      Religion..2011..Hindu        0.06049182 randomForest
151                                              Household.Composition..2011..Percentages.One.person.household        0.06049665 randomForest
152                                                                                    House.Prices.Sales.2009        0.06049784 randomForest
153                                                                              House.Prices.Sales.2011...130        0.06049885                                                                  Health..2011.Census..Very.good.health....        0.06051842 randomForest
156                                            Low.Birth.Weight.Births..2007.2011..Low.Birth.Weight.Births....        0.06052278 randomForest
157                                                                       Health..2011.Census..Very.bad.health        0.06052527 randomForest
158                                                                           Health..2011.Census..Fair.health        0.06052537 randomForest
159 randomForest
161                                                         Ethnic.Group..2011.Census..Asian.Asian.British....        0.06054116 randomForest
162                                           Low.Birth.Weight.Births..2007.2011..UCL...Upper.confidence.limit        0.06055614 randomForest
163                                           Ethnic.Group..2011.Census..Black.African.Caribbean.Black.British        0.06056211 randomForest
164                          Qualifications..2011.Census..Highest.level.of.qualification..Other.qualifications        0.06056219 randomForest
165                                                                        Mid.year.Estimates.2012..by.age.0.4        0.06056244 randomForest
166                                                              Population.Density.Persons.per.hectare..2012.        0.06057661 randomForest
167                                                                    Religion..2011..Religion.not.stated....        0.06058630 randomForest
168                                                                        Religion..2011..Religion.not.stated        0.06058679 randomForest
169                                                                                       Religion..2011..Sikh        0.06059155 randomForest
170                                                                          Incidence.of.Cancer.Breast.Cancer        0.06062165 randomForest
171                                                                 Country.of.Birth..2011..United.Kingdom....        0.06062725 randomForest
172                                                                            Ethnic.Group..2011.Census..BAME        0.06066563 randomForest
173                                                                 Country.of.Birth..2011..Not.United.Kingdom        0.06068361 randomForest
174                                                                  Mid.year.Estimates.2012..by.age...0.to.14        0.06068807 randomForest
175                                                         Tenure..2011..Owned..Owned.with.a.mortgage.or.loan        0.06068995 randomForest
176                                                    Ethnic.Group..2011.Census..Mixed.multiple.ethnic.groups        0.06069163 randomForest
177                        Qualifications..2011.Census..Highest.level.of.qualification..Level.3.qualifications        0.06072193 randomForest
178                                        Car.or.van.availability..2011.Census..1.car.or.van.in.household....        0.06074983 randomForest
179                                                                      Mid.year.Estimates.2012..by.age.15.19        0.06075380 randomForest
180        Household.Language..2011....of.people.aged.16.and.over.in.household.have.English.as.a.main.language        0.06075892 randomForest
181                                                                            Health..2011.Census..Bad.health        0.06076332 randomForest
182                                                   Health..2011.Census..Day.to.day.activities.limited.a.lot        0.06077496 randomForest
183                                       Ethnic.Group..2011.Census..Black.African.Caribbean.Black.British....        0.06082769 randomForest
184                           Household.Language..2011..No.people.in.household.have.English.as.a.main.language        0.06085115 randomForest
185                                         Car.or.van.availability..2011.Census..No.cars.or.vans.in.household        0.06085605 randomForest
186                                     Car.or.van.availability..2011.Census..No.cars.or.vans.in.household....        0.06087480 randomForest
187                                                                       Health..2011.Census..Good.health....        0.06088495 randomForest
188     Household.Language..2011....of.households.where.no.people.in.household.have.English.as.a.main.language        0.06090083                                                                       Ethnic.Group..2011.Census..White....        0.06100824 randomForest
191                                                                                    Life.Expectancy.Females        0.06113049 randomForest
192                                               Economic.Activity..2011.Census..Economically.inactive..Total        0.06114768 randomForest
193                                                                          Age.Structure..2011.Census..16.29        0.06116905 randomForest
194                                                                        Ethnic.Group..2011.Census..BAME....        0.06120881 randomForest
195                                                                                      Life.Expectancy.Males        0.06122637 randomForest
196
198                                                                                    Incidence.of.Cancer.All        0.06157997 randomForest
199                                                                                         RPDburglaryShifted
201                                                                            Road.Casualties.2012.2012.Total        0.06221397 randomForest
202                                                                               Religion..2011..Buddhist....        0.06230384 randomForest        0.06238647 randomForest
205                                                                            Road.Casualties.2011.2011.Total        0.06269966 randomForest
206                                                                            Road.Casualties.2010.2010.Total        0.06275241 randomForest
207                                                                                   Religion..2011..Buddhist        0.06309183 randomForest
208                                                              Ethnic.Group..2011.Census..Other.ethnic.group        0.06343477 randomForest
209                                                                                Road.Casualties.2010.Slight        0.06363878 randomForest
210                                                          Ethnic.Group..2011.Census..Other.ethnic.group....        0.06459224 randomForest
211                                                                                           total_burglaries        0.06882403 randomForest
212                                                                                            total_robberies randomForest
plot(model_parts_rob, max_vars=25)

pdp_rob <- model_profile(rf_explainer_robbery)
plot(pdp_rob, variables="total_robberies")

plot(pdp_rob, variables="total_burglaries")

The effect of historic crime effects again appears like a reliable predictor of a robbery covid shift: those MSOAs with the highest number of burglaries and robberies see strong decreases in robbery (though the association with burglary is not clear cut, suggesting other interaction effects may be driving this)

plot(pdp_rob, variables="Road.Casualties.2011.2011.Total")

Road casualties is another strong relationship. This could be a proxy for deprivation, but I suggest this is more down to geographic features - road casualties are probably rarer in denser urban environments, most likely to be affected by lockdown.

plot(pdp_rob, variables="Ethnic.Group..2011.Census..Other.ethnic.group....")

hist(data$Ethnic.Group..2011.Census..Other.ethnic.group....)

Finally, we see a demographic predictor linked to “other ethnic group”. I’m not clear how to interpret this, but it suggests that those MSOAs that are most diverse (and have the largest representation by these ethnic groups) experienced the strongest decreases in robbery during lockdown.

Together, these analyses suggest that the crime drop for robbery and burglary during national lockdown was significantly affected by distinct local factors. For both offences, historical crime trends play a role, with high crime areas experiencing a relatively larger drop in both burglary and robbery.

Beyond that, the drivers vary for each offence type: burglary was driven by the composition of the residential population, with heavily residential areas, and areas with a relatively “stable” population as measured by low housing sales also saw larger decrease - this is likely due to the increased number of empty residential properties.

Robbery decreases conversely, are well associated with high numbers of road casualties, as well as the ethnic makeup of the local population - this is likely due to an association with denser, more urban areas, with lower street speeds, and a possible link to deprivation, whereby minority population were least able to work from home, and were likely to still present as available targets for robbery.

---
title: "Learning R - Exploring the COVID Crime Effect in London"
output: html_notebook
---
## Exploring Predictors of COVID Crime Shifts
The lockdown and social distancing measures that were brought in throughout the world to tackle COVID in 2020 have had a significant, widespread effect on crime. In this notebook, I use public London crime data on robbery and burglary to examine where this "COVID crime shift" was strongest, and whether any specific drivers or correlates can be identified.  

Our findings suggest that the relative change in burglary and robbery trends during "lockdown" in April and May 2020 was heavily affected by local characteristics: areas with a high residential population saw teh sharpest decreases in burglary (likely due to a reduction in available targets) while the reduction in robberies instead seem to be driven by geographic features and proxy indicators of deprivation (potentially suggesting more available targets for robbery in communities least able to work for from).

The primary purpose of this exercise was to learn R - I've previously worked entirely in Python, which is more than sufficient 99% of the time, but has at times proved a blocker when I want to tackle some more experimental geospatial methods or tools geared towards the academic community.  With that in mind, this is likely to be a little messy, and I'll aim to condense my main lessons into a blog post in the future. The models are not heavily tuned (aiming to explore correlates rather than provide accurate predictions) and certain predictors are likely to correlate with each other, and as such likely do not imply direct causations.

#### Resources I've used
- Matt Ashby Crime Mapping course: https://github.com/mpjashby/crimemapping/
- Spatial Modelling for Data Scientists: https://gdsl-ul.github.io/san/
- R for Data Science: https://r4ds.had.co.nz/index.html
- Geocomputation with R: https://geocompr.robinlovelace.net/



### Tasks

1. Ingest burglary and robbery data and assign to MSOA
2. Predict trend by MSOA
3. Identify COVID effect/error by MSOA
4. Model

### Data
In this exercise, I'm using three years of Metropolitan Police Service data from data.police.uk - I've downloaded these manually rather than using their API.

## 1. Ingest burglary and robbery data and assign to MSOA
Unlike Python has the benefit of being "focused" - it's primaryily a tool for academics/scientists, rather than a programming language. That means the eco-system is refreshingly helpful: at first glance, there is one primary IDE, one package library, and it all works. Unlike Python, most libraries are imported globally, and that works okay...*mostly*

[MSOAs are geographical units specifically designed for analysis, and to be comparable: they all have an average population of just over 8,000.](https://www.ons.gov.uk/methodology/geography/ukgeographies/censusgeography#output-area-oa)

```{r, results='hide'}
# Data manipulation, transformation and visualisation
library(tidyverse)
# Nice tables
library(kableExtra)
# Simple features (a standardised way to encode vector data ie. points, lines, polygons)
library(sf) 
# Spatial objects conversion
library(sp) 
# Thematic maps
library(tmap) 
# Colour palettes
library(RColorBrewer) 
# More colour palettes
library(viridis)
#ggplot organiastion
library(ggpubr)


library(raster)  # raster data
library(rgdal)  # input/output, projections
library(rgeos)  # geometry ops
library(spdep)  # spatial dependence

library(lubridate) #date and time

#random forest and metrics
library(Metrics)
library(caret)
library(randomForest)
require(caTools)
library(DALEX)
library(dplyr)



#correlation matrix
library(corrr)



```

Importing data from CSV files behaves quite similarly to Python. To build our process, we'll start by taking one month of crime data, exploring it, and writing all our steps for automation.

```{r}
test_df <- read.csv("crimes/2018-01/2018-01-metropolitan-street.csv")
test_df

```
Our crime is categories according to the Home Office major crime types, and like Python, we can list them all through the "unique" function. Here I'll be focusing on robbery and burglary: two crime types that are heavily reliant on encountering victim's in public spaces, and as such should be affected by the "COVID effect".

```{r}
unique(test_df["Crime.type"])
```
To avoid this getting particularly computationally intensive, let's write a function to pull out robberies and burglaries, and assign them a specific MSOA. Then we can iterate over all our months and get monthly counts for each offence type.

```{r}
subset_df <- filter(test_df, Crime.type=="Burglary" | Crime.type=="Robbery")
subset_df
```
Our single month of data contains 10,501 crimes.

There are R/Python quirks that will take some getting used to. While in Python, most columns can be referenced through their string name (["name"]), R seems somewhat fussier. Other than that, the move from one to another is largely intuitive.

We now need to link this to our spatial data. We use the MSOA borders provided by MOPAC, and use the UK National Grid coordinate system. Police.uk does not use that system, so we'll need to reproject our crime data.

```{r}
lsoa_borders <- st_read("msoa_borders/MSOA_2011_London_gen_MHW.tab", crs=27700)
lsoa_borders

```
Unlike our previous dataframes, this isn't "tidy" (due to a slightly different format containing geographical data)

```{r}
plot(lsoa_borders)
```
Before we can link our crimes to MSOA, we'll need to ensure identical coordinate systems, but before we do that, we'll need to erase any missing values.


```{r}
#count missing values in the longitude column
sum(is.na(subset_df["Longitude"]))
```

As such, we have 82 crimes with no geographic identifiers, which we remove from our analysis.

```{r}
clean_df <- subset_df[!rowSums(is.na(subset_df["Longitude"])), ]
clean_df
```
We can now convert our crime data to spacial data, using our longitude and latitude coordinates - this allows us to quickly plot our data, and confirm it looks right.

```{r}

subset_spatial <- st_as_sf(clean_df, coords = c("Longitude", "Latitude"), 
                      crs = 4326, remove = FALSE)

subset_spatial
```


```{r}
plot(subset_spatial)
```
Success! That looks faintly promising.  Now, let's figure out how to re-project.

```{r}

latlong = "+init=epsg:4326"
ukgrid = "+init=epsg:27700"

```

```{r}
subset_osgb <- st_transform(subset_spatial, ukgrid)
subset_osgb
```

We now run a "spatial join": assigning an MSOA to each of our crimes, based on the MSOA border map they are within, and combining these as one table.

```{r}
crime_with_msoa <- st_join(subset_osgb, lsoa_borders["MSOA11CD"])
crime_with_msoa
```
That has worked: each crime is now assigned to an MSOA. We can now group our table by count of MSOA, to obtain the monthly count of

```{r}
msoa_list<- crime_with_msoa %>%
  group_by(MSOA11CD, Crime.type) %>%
  summarize(count_by_msoa = n())

msoa_list
```
We now have a count for each, and we can remove the geometry data before automating our process.

```{r}
msoa_pivot_tibble <- as_tibble(msoa_list)
msoa_pivot_tibble <- msoa_pivot_tibble[0:3]
msoa_pivot_tibble

```

As a final stage prior to processing the rest of our data, we will fill any missing msoa/month combinations with a "0", to ensure consistent trends.

```{r}
#creating a df with all msoa names, for robbery and burglary
msoa_zero_df_robbery <- unique(as_tibble(lsoa_borders)["MSOA11CD"])
msoa_zero_df_burglary <- unique(as_tibble(lsoa_borders)["MSOA11CD"])

#adding our crime type column 
msoa_zero_df_burglary["Crime.type"] = "Burglary"
msoa_zero_df_robbery["Crime.type"] = "Robbery"

#Creating a "count" column identical to our pivot, and filling it with 0
msoa_zero_df_burglary["count_by_msoa"] = as.numeric(0)
msoa_zero_df_robbery["count_by_msoa"] = as.numeric(0)

#combine both
duplicate_concat <- rbind(msoa_zero_df_robbery, msoa_zero_df_burglary)

#add our duplicates to our original table
df_with_dups <- rbind(msoa_pivot_tibble, duplicate_concat)


#creating a filter for duplicates columns, which should ignore the first instance
dup_filters <- duplicated(df_with_dups[0:2])


#bring it all back together
monthly_df <- filter(df_with_dups, !dup_filters)
monthly_df

#select the first unique value of months in the original dataframe
month <- unique(test_df["Month"])[1,1]
monthly_df["Month"] <- month
monthly_df

```
we now have our basic functionality to create a time series for both crime types, by MSOA - a count of each type, and the month. 

I can now bring all my previous work together into a function, which we can use to automate the process.

```{r}
#quick initial function to generate our MSOA borde spatial frame, to avoid it sitting in the initial frame and gobbling loads of memory.
generate_msoa_borders <- function(file){
  msoa_borders <- st_read(file, crs=27700)
  return(msoa_borders)
}

make_month_pivot <- function(file){
  #define our CRS
  latlong = "+init=epsg:4326"
  ukgrid = "+init=epsg:27700"
  #read our crime from the file
  test_df <- read.csv(file)
  #select only our target crime types
  subset_df <- filter(test_df, Crime.type=="Burglary" | Crime.type=="Robbery")
  #remove any rows with a long/lat coordinate
  clean_df <- subset_df[!rowSums(is.na(subset_df["Longitude"])), ]
  #generate a spatial df
  subset_spatial <- st_as_sf(clean_df, coords = c("Longitude", "Latitude"), 
                      crs = 4326, remove = FALSE)
  #reproject to uk grid coords
  subset_osgb <- st_transform(subset_spatial, ukgrid)
  #spatially join to assign to an MSOA
  crime_with_msoa <- st_join(subset_osgb, msoa_borders["MSOA11CD"])
  #summarise by count of MSOA
  msoa_list<- crime_with_msoa %>%
    group_by(MSOA11CD, Crime.type) %>%
    summarize(count_by_msoa = n())
  #return to a non-geographic msoa
  msoa_pivot_tibble <- as_tibble(msoa_list)
  msoa_pivot_tibble <- msoa_pivot_tibble[0:3]
  #creating a df with all msoa names, for robbery and burglary
  msoa_zero_df_robbery <- unique(as_tibble(msoa_borders)["MSOA11CD"])
  msoa_zero_df_burglary <- unique(as_tibble(msoa_borders)["MSOA11CD"])
  #adding our crime type column 
  msoa_zero_df_burglary["Crime.type"] = "Burglary"
  msoa_zero_df_robbery["Crime.type"] = "Robbery"
  #Creating a "count" column identical to our pivot, and filling it with 0
  msoa_zero_df_burglary["count_by_msoa"] = as.numeric(0)
  msoa_zero_df_robbery["count_by_msoa"] = as.numeric(0)
  duplicate_concat <- rbind(msoa_zero_df_robbery, msoa_zero_df_burglary)
  df_with_dups <- rbind(msoa_pivot_tibble, duplicate_concat)
  #creating a filter for duplicates columns, which should ignore the first instance
  dup_filters <- duplicated(df_with_dups[0:2])
  monthly_df <- filter(df_with_dups, !dup_filters)
  #re-add our month column
  month <- unique(test_df["Month"])[1,1]
  monthly_df["Month"] <- month
  return(monthly_df)
}
```

We now have a rudimentary tooling pipeline, which we can iterate over our subfolders to aggregate our data (in hindset, I probably should have explored the API options).

  
```{r, results='hide'}
#create empty dataframe to bring together our data
empty_df <- tibble(
MSOA11CD = "", 
Crime.type= "",
count_by_msoa= "",
Month= ""
)

#re-ingest our MSOA data
msoa_borders <- generate_msoa_borders("msoa_borders/MSOA_2011_London_gen_MHW.tab")
```

Our function will iterate over each file, add them to our empty table, until each is complete (and we have a single, aggregated file)

```{r, results='hide'}
subfiles <- list.files(path = "crimes", recursive=T)

for (file in subfiles){
  folder_subdir <- "crimes/"
  #concatenate to get our total subfolder directory - hacky but will work here.
  sub_path <- paste(folder_subdir, file, sep="")
  monthly_df <- make_month_pivot(sub_path)
  empty_df <- rbind(empty_df, monthly_df)
}

```


```{r}
empty_df
```
We now have a combined dataframe of 71,848 rows, from January 2018 through December 2020.

```{r}
unique(empty_df["Month"])
```
From a practical perspective, that was slightly more painful than I expected - I'm not sure if data-wrangling is less intuitive in R, or it's just practice, but it's noticeable how easy use cases are less easily accessible as tutorials (probably due to the different user base
)


```{r}
#saving file to CSV
#write.csv(empty_df,"msoa_crime_matrix.csv")

```



## 2. Predict trend by MSOA
#### Visualisation and Exploration
With our data now cleaned and aggregated, we can focus on the more interesting part - forecasting our "expected" pandemic crime, and examining how much it diverges from our "actual" crime.

```{r}
empty_df <- read.csv("msoa_crime_matrix.csv")
empty_df <- empty_df[2:70848,2:5]
empty_df
```


Before going any further, let's use this to explore and visualise the distribution of robbery and burglary across time and space during our "pre-pandemic" period, in March 2020 - based on London mobility indicators, this is when movement accross London began to be heavily affected, and the disruption was most notable in April

![London mobility data](london_mobility.png)

```{r}
burglary_df<-empty_df

#add a "1" so our month can be converted to a full date
burglary_df$DateString <- paste(burglary_df$Month, "-01", sep="")

#convert to date format
burglary_df$DateClean <- ymd(burglary_df$DateString)

#filter out only burglary prior to the pandemic
burglaryExplore <- filter(burglary_df,  DateClean < "2020-03-01" & Crime.type=="Burglary")

burglaryExplore
```


Looking at the aggregate counts of burglary across London, a visual observation suggests yearly trends (which we'll have to consider in our forecast), which sharp peaks during the Winter months and the lowest numbers in summer (when the days are longest).
```{r}
#group burglary count by months and plot
burglary_by_month <- burglaryExplore %>%
  group_by(DateClean) %>%
  summarize(total_burglaries = sum(count_by_msoa))

ggplot(burglary_by_month, aes(x=DateClean, y=total_burglaries)) +
  geom_line()
```

To observe how crime counts are distributed in space, let's map both counts by MSOA. As  previously mentioned, MSOAs are designed to be comparable units, at least from a population perspective - we don't need to produce per population rates. 


```{r, fig.width = 13}
burglary_by_msoa <- burglaryExplore %>%
  group_by(MSOA11CD) %>%
  summarize(total_burglaries = sum(count_by_msoa))

#we join our burglary counts to their geographic msoa
burglary_map <- left_join(lsoa_borders, burglary_by_msoa, by = "MSOA11CD")

#user brewer colour palette https://colorbrewer2.org
pal <- brewer.pal(5,"BuGn")

#create our map, and add the layout options
burglary_map <-tm_shape(burglary_map) +
  tm_fill(col = "total_burglaries", title = "Total Burglary Count by MSOA", style="quantile", palette="BuGn") +
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")

robbery_df<-empty_df

robbery_df$DateString <- paste(robbery_df$Month, "-01", sep="")
robbery_df$DateClean <- ymd(robbery_df$DateString)
robberyExplore <- filter(robbery_df,  DateClean < "2020-03-01" & Crime.type=="Robbery")

robbery_by_msoa <- robberyExplore %>%
  group_by(MSOA11CD) %>%
  summarize(total_robberies = sum(count_by_msoa))

robbery_map <- left_join(lsoa_borders, robbery_by_msoa, by = "MSOA11CD")

pal <- brewer.pal(5,"BuGn")


robbery_map <-tm_shape(robbery_map) +
  tm_fill(col = "total_robberies", title = "Total Robbery Count by MSOA", style="quantile", palette="BuGn") +
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")


#arrange the maps together
tmap_arrange(burglary_map, robbery_map, nrow = 2)
```

We notice that robbery is noticeably more concentrated in central London, with burglary remaining quite common across the city. That said, there are also obvious spatial patterns here - these crimes are clustered in certain geographies. 

#### Modelling 
We can now begin the forecasting process. To design our process, we'll start by focusing on a single MSOA - the first in our dataset, [E02000001, or the City of London.](https://findthatpostcode.uk/areas/E02000001.html)

```{r}
single_msoa_df <- filter(empty_df, MSOA11CD == "E02000001" & Crime.type=="Burglary")

#we add a 01 to our date to ensure R recognises the date format
single_msoa_df$DateString <- paste(single_msoa_df$Month, "-01")


single_msoa_df$DateClean <- ymd(single_msoa_df$DateString)
single_msoa_df
```
From a forecasting/time-series perspective, this is a very small dataset - 36 monthly observations. We will be shrinking this further to only 26 by focusing on data prior to March 2020, when the COVID crime impact is felt. This significantly limits our forecasting options, and will impact accuracy, if we treat each MSOA in isolation - we could explore some sort of Vector Autoregressive Model to limit this, but given that we're then going to be exploring the error of all our models in aggregation, this isn't crucial. Our focus is on models that we can accurately deploy without needing to tune each of them individually, and that can capture the seasonal trend, and generate reliable predictions on our limited dataset. 

Given these limitations, I've opted for [the Prophet algorith.](https://facebook.github.io/prophet/) While it's more opaque than a auto-arima or VAR model, it works well with monthly data, and extracting seasonal trends. It also requires very little tuning.

As such, we'll extract our "training set" prior to March, and start forecasting.

```{r}

training_set <- filter(single_msoa_df, DateClean < "2020-03-01")

training_df <- tibble(
  ds=training_set$DateClean,
  y=training_set$count_by_msoa
)
training_df
```

```{r, results='hide'}
library(prophet)
m <- prophet(training_df)

```
For now, we'll forecast on a 6 month horizon - we obviously wouldn't expect it to be accurate that far into the future.

```{r}
#prophet generates a future dataframe using our data, for 6 mperiods
future <- make_future_dataframe(m, periods = 6, freq = 'month')


forecast <- predict(m, future)

plot(m, forecast)

```
As we can see, the model seems consistent on a short horizon, and gets very wide as it goes further into the future. More importantly however, it has extracted a yearly seasonal compontent - the summer decrease we identified previously - as well as a long term trend.  

```{r}

prophet_plot_components(m, forecast)
```
These predictions seem far-fetched, but remember we will be observing a London wide error rate. As such, we must now isolate our "pandemic period" - which we define as April and May 2020 - and compare the predicted crime counts to the actual crime counts to obtain a metric of our "COVID crime shift", or our error rate.

```{r}


forecast$Month <- month(forecast$ds)
forecast$Year <- year(forecast$ds)


this_year <- filter(forecast, Year > 2019)
peak_pandemic <- filter(this_year, Month== 4 | Month== 5 )

predictionPivot <- peak_pandemic %>%
  group_by(Month) %>%
  summarize(predicted_burglary = mean(yhat))


single_msoa_df$MonthNum <- month(single_msoa_df$DateClean)
single_msoa_df$YearNum <- year(single_msoa_df$DateClean)

this_year_actual <- filter(single_msoa_df, YearNum > 2019)
peak_pandemic_actual <- filter(this_year_actual, MonthNum== 4 | MonthNum== 5 )

actual_burglary <- sum(peak_pandemic_actual$count_by_msoa)
pred_burglary <- sum(predictionPivot$predicted_burglary)

error <- actual_burglary - pred_burglary
percentage_error <- error / pred_burglary 

print("Burglary Count")
print(actual_burglary)
print("Predicted")
print(pred_burglary)

print("Actual Error")
print(error)
print("Percentage Error")
print(percentage_error)
```
In this MSOA, our model predicted nearly 8 burglaries would occur in these two months, based on pre-pandemic trends. In reality, 1 took place - a large error rate, suggesting a strong "COVID effect".

This process can now be replicated for every MSOA in London, to obtain this metric for each MSOA.

```{r, results='hide'}


msoa_error_tibble <- tibble(
MSOA11CD = "", 
burglaryActual= "",
burglaryPredicted= "",
burglaryError= "",
burglaryPercentError="",
robberyActual= "",
robberyPredicted= "",
robberyError= "",
robberyPercentError=""
)

calculate_error <- function(msoaName){
  #select only burglary and our msoa
  single_msoa_df <- filter(empty_df, MSOA11CD == msoaName & Crime.type=="Burglary")
  #clean date date
  single_msoa_df$DateString <- paste(single_msoa_df$Month, "-01")
  single_msoa_df$DateClean <- ymd(single_msoa_df$DateString)
  #generate training set up until March
  training_set <- filter(single_msoa_df, DateClean < "2020-03-01")
  #prepare for Prophet
  training_df <- tibble(
    ds=training_set$DateClean,
    y=training_set$count_by_msoa)
  #start and predict prophet for 6 months
  m <- prophet(training_df)
  future <- make_future_dataframe(m, periods = 6, freq = 'month')
  forecast <- predict(m, future)
  forecast$Month <- month(forecast$ds)
  forecast$Year <- year(forecast$ds)
  #aggregate forecasts and actual crime
  this_year <- filter(forecast, Year > 2019)
  peak_pandemic <- filter(this_year, Month== 4 | Month== 5 )
  predictionPivot <- peak_pandemic %>%
    group_by(Month) %>%
    summarize(predicted_burglary = mean(yhat))

  single_msoa_df$MonthNum <- month(single_msoa_df$DateClean)
  single_msoa_df$YearNum <- year(single_msoa_df$DateClean)
  #generate error rates
  this_year_actual <- filter(single_msoa_df, YearNum > 2019)
  peak_pandemic_actual <- filter(this_year_actual, MonthNum== 4 | MonthNum== 5 )
  actual_burglary <- sum(peak_pandemic_actual$count_by_msoa)
  pred_burglary <- sum(predictionPivot$predicted_burglary)
  error_burg <- actual_burglary - pred_burglary
  percentage_error_burg <- error_burg / pred_burglary 
  
  #now repeat for robbery
  
  single_msoa_df <- filter(empty_df, MSOA11CD == msoaName & Crime.type=="Robbery")
  single_msoa_df$DateString <- paste(single_msoa_df$Month, "-01")
  single_msoa_df$DateClean <- ymd(single_msoa_df$DateString)
  training_set <- filter(single_msoa_df, DateClean < "2020-03-01")
  training_df <- tibble(
    ds=training_set$DateClean,
    y=training_set$count_by_msoa)
  m <- prophet(training_df)
  future <- make_future_dataframe(m, periods = 6, freq = 'month')
  forecast <- predict(m, future)
  forecast$Month <- month(forecast$ds)
  forecast$Year <- year(forecast$ds)
  this_year <- filter(forecast, Year > 2019)
  peak_pandemic <- filter(this_year, Month== 4 | Month== 5 )
  predictionPivot <- peak_pandemic %>%
    group_by(Month) %>%
    summarize(predicted_burglary = mean(yhat))

  single_msoa_df$MonthNum <- month(single_msoa_df$DateClean)
  single_msoa_df$YearNum <- year(single_msoa_df$DateClean)

  this_year_actual <- filter(single_msoa_df, YearNum > 2019)
  peak_pandemic_actual <- filter(this_year_actual, MonthNum== 4 | MonthNum== 5 )
  actual_robbery <- sum(peak_pandemic_actual$count_by_msoa)
  pred_robbery <- sum(predictionPivot$predicted_burglary)
  error_rob <- actual_robbery - pred_robbery
  percentage_error_rob <- error_rob / pred_robbery 
  
  #create our output dataframe and return it
  
  msoa_error_tibble <- tibble(
    MSOA11CD = msoaName, 
    burglaryActual= actual_burglary,
    burglaryPredicted= pred_burglary,
    burglaryError= error_burg,
    burglaryPercentError = percentage_error_burg,
    robberyActual= actual_robbery,
    robberyPredicted= pred_robbery,
    robberyError= error_rob,
    robberyPercentError=percentage_error_rob
    )

  return(msoa_error_tibble)
}

for (msoa in unique(empty_df$MSOA11CD)){
  iterated_msoa_df <- calculate_error(msoa)
  msoa_error_tibble <- rbind(msoa_error_tibble, iterated_msoa_df)
  
}


```




```{r}
msoa_error_tibble
```

Our process has completed: we have a "COVID shift" measure for all of London.

## 3. Measuring Local COVID Crime Shifts

We now need to use our forecasts to measure the "error" - this should provide an indication of the "COVID Crime Shift", or how much the actual crime diverted from the previous forecasts.

I explored various avenues for this: the ideal solution would be a relative rate of the error, as MSOAs with large crime numbers will likely generate large errors, and so a rate would be ideal, though this is complicated by our erratic prediction and mix of positive and negative numbers.

Our final solution has explored two options:
- the absolute error number
- the relative error once the crime and predictions have been transformed (by adding 50)

We visualise and describe these statistics first to ensure they appear sensible.


```{r}
#write_csv(msoa_error_tibble, "msoa_error_table2.csv")
```

```{r}
msoa_error_tibble <- read_csv("msoa_error_table2.csv")
#msoa_error_tibble<- msoa_error_table[2:980,]
msoa_error_tibble[,2:9] <- lapply(msoa_error_tibble[,2:9], as.numeric)

msoa_error_tibble <- msoa_error_tibble[2:980, ]

msoa_error_tibble <- left_join(msoa_error_tibble, robbery_by_msoa, by = "MSOA11CD")
msoa_error_tibble <- left_join(msoa_error_tibble, burglary_by_msoa, by = "MSOA11CD")


```


```{r}

msoa_error_tibble$RPDBurglary <- (msoa_error_tibble$burglaryActual - msoa_error_tibble$burglaryPredicted)/((msoa_error_tibble$burglaryPredicted + msoa_error_tibble$burglaryActual)/2)

msoa_error_tibble$RPDRobbery <- (msoa_error_tibble$robberyActual - msoa_error_tibble$robberyPredicted)/((msoa_error_tibble$robberyPredicted + msoa_error_tibble$robberyActual)/2)

msoa_error_tibble$robberyActualShifted <- msoa_error_tibble$robberyActual + 50
msoa_error_tibble$robberyPredictedShifted <- msoa_error_tibble$robberyPredicted + 50


msoa_error_tibble$RPDRobberyShifted <- (msoa_error_tibble$robberyActualShifted - msoa_error_tibble$robberyPredictedShifted)/((msoa_error_tibble$robberyPredictedShifted + msoa_error_tibble$robberyActualShifted)/2)

msoa_error_tibble$burglaryActualShifted <- msoa_error_tibble$burglaryActual + 50
msoa_error_tibble$burglaryPredictedShifted <- msoa_error_tibble$burglaryPredicted + 50


msoa_error_tibble$RPDburglaryShifted <- (msoa_error_tibble$burglaryActualShifted - msoa_error_tibble$burglaryPredictedShifted)/((msoa_error_tibble$burglaryPredictedShifted + msoa_error_tibble$burglaryActualShifted)/2)


```

```{r}
print("Burglary Error")
summary(msoa_error_tibble$burglaryError)
print("Burglary Relative Error")
summary(msoa_error_tibble$RPDburglaryShifted)
print("Robbery Error")
summary(msoa_error_tibble$robberyError)
print("Robbery Relative Error")
summary(msoa_error_tibble$RPDRobberyShifted)

```
As we can see, the average London MSOA experienced a negative COVID crime shift for both burglary and robbery, but this is far from equally distributed - at the extremes, some areas actually see large increases on our predicted values. 

```{r , fig.width = 13}

burg_hist <- ggplot(msoa_error_tibble, aes(x=burglaryError)) + geom_histogram()
rob_hist <-ggplot(msoa_error_tibble, aes(x=robberyError)) + geom_histogram()
burg_r_hist <- ggplot(msoa_error_tibble, aes(x=RPDburglaryShifted)) + geom_histogram()
rob_r_hist <- ggplot(msoa_error_tibble, aes(x=RPDRobberyShifted)) + geom_histogram()
scatter <- ggplot(msoa_error_tibble, aes(x = RPDRobberyShifted, y = RPDburglaryShifted)) +
  geom_point()

r_scatter <- ggplot(msoa_error_tibble, aes(x = robberyError, y = burglaryError)) +
  geom_point()

ggarrange(rob_hist, burg_hist, rob_r_hist, burg_r_hist,scatter, r_scatter, ncol=2, nrow=3 )


```
Our shifted relative error rate seems to function as intended: while there are still outliers, they are more concentrated than they are for the pure error term, and the overall distribution is more focused, while still indicating the direction and relative strength of our COVID effect.

Let's map this effect visually, and see if any particular areas stand out.

```{r , fig.width = 13}
#re-ingest our geographic MSOA borders
msoa_borders <- st_read("msoa_borders/MSOA_2011_London_gen_MHW.tab", crs=27700)

geographic_error_map <- left_join(msoa_borders, msoa_error_tibble, by = "MSOA11CD")

burg_map <- tm_shape(geographic_error_map) +
  tm_fill(col = "robberyError", title = "Robbery Error", palette="-PuOr")+
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")
rob_map <-tm_shape(geographic_error_map) +
  tm_fill(col = "burglaryError", title = "Burglary  Error", palette="-PuOr")+
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")


burg_map_rate <- tm_shape(geographic_error_map) +
  tm_fill(col = "RPDRobberyShifted", title = "Robbery Error Relative", palette="-PuOr")+
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")
rob_map_rate <-tm_shape(geographic_error_map) +
  tm_fill(col = "RPDburglaryShifted", title = "Burglary  Error Relative", palette="-PuOr")+
  tm_layout(legend.outside = TRUE, legend.outside.position = "right")


tmap_arrange(burg_map, rob_map, burg_map_rate, rob_map_rate , nrow = 2, ncol=2)

```
It's hard to identify any obvious effect visually, but we do notice that while central London sees some very strong reductions, it also sees some increases.  Conversely, the outskirts of London (notably to the south and West) are a near continuous area of large decreases. The effect does vary by offence type, but the pattern seen in South and West London appears broadly consistent.

## 4. Identifying Correlates and Modelling

We've identified that the COVID crime effect was felt unequally accross London, and varies by offence type. To finalise our project, we will be linking our data to [demographic data provided by MOPAC](https://data.london.gov.uk/dataset/msoa-atlas), and aiming to use it to identify correlates to our "covid shift", and hopefully build models disentangling the effect.

```{r}
library(readxl)
#ingest ATLAS
msoa_atlas <- read_excel("msoa_atlas/msoa-data.xls")

#join by MSOA
geographic_msoa_matrix <- left_join(geographic_error_map, msoa_atlas, by = "MSOA11CD")

#convert to tibble
msoa_matrix_tbl <- as_tibble(geographic_msoa_matrix)
write_csv(msoa_matrix_tbl, "msoa_matrix.csv")


#select only numeric data
msoa_matrix_numeric <-dplyr::select_if(msoa_matrix_tbl, is.numeric)
msoa_matrix_numeric
```
Having now ingested and linked our data, we begin by exploring the factors most highly correlated with our relative error rates.

```{r, results='hide'}

corr_df <- correlate(dplyr::select_if(msoa_matrix_tbl, is.numeric), quiet = TRUE)

options(scipen=999)
```
Starting by our relative robbery error, a few interesting correlates stand out:
- road traffic casualties
- burglary numbers
- the number of dwellings with no usual residents, and the number of commercial residents
- households with no cars
- the age composition of the area
- general deprivation indicators (such as the proportion of households with central heating)

```{r}
#show only correlates with an absolute value higher than 0.2
#filter(dplyr::select(corr_df[order(corr_df$RPDRobberyShifted),] , term, RPDRobberyShifted), RPDRobberyShifted < -0.2 | RPDRobberyShifted > 0.2)
#filter(dplyr::select(corr_df[order(corr_df$RPDRobberyShifted),] , term, RPDRobberyShifted), RPDRobberyShifted < -0.2 | RPDRobberyShifted > 0.2)
high_corr_rob <- filter(dplyr::select(corr_df, term, RPDRobberyShifted), RPDRobberyShifted < -0.15 | RPDRobberyShifted > 0.15)

high_corr_rob[order(high_corr_rob$RPDRobberyShifted),]

```
The correlations for burglary are weaker - only a few have an absolute value higher than 0.2 - but a few stand out:
- households with no residents
- high robbery numbers
- house prices 

```{r}

high_corr_burg <- filter(dplyr::select(corr_df, term, RPDburglaryShifted), RPDburglaryShifted < -0.15 | RPDburglaryShifted > 0.15)

high_corr_burg[order(high_corr_burg$RPDburglaryShifted),]

```
These correlates suggest we can model this shift - this is likely to prove more reliable for robbery (where the correlations are stronger), and seem linked to usual resident population(as measured by household composition), deprivation (through various proxy indicators such as central heating presence or housing type), and general crime patterns (through total burglary and robbery numbers)

We will take two approaches for modelling: a simple regression (to identify strong links) and random forest regressors (to identify non-linear associations)

### Simple Regression

We begin through the use of simple OLS regression. This is a linear model that has large limitations for modelling complex relationships, but can be an effective first step, effectively with a few transformations.

R does not cope well with blank spaces in terms, so we'll extract and rename our key correlates.

```{r}

#make copy of df and rename 

msoa_copy <- msoa_matrix_numeric

names(msoa_copy)[names(msoa_copy) == "Dwelling type (2011) Household spaces with no usual residents"] <- "DwellingNoResidents"
names(msoa_copy)[names(msoa_copy) == "House Prices Median House Price (£) 2010"] <- "MedianHousePrice"
names(msoa_copy)[names(msoa_copy) == "Dwelling type (2011) Flat, maisonette or apartment"] <- "FlatAprt"
names(msoa_copy)[names(msoa_copy) == "Qualifications (2011 Census) Schoolchildren and full-time students: Age 18 and over"] <- "fullTimeStudents"
names(msoa_copy)[names(msoa_copy) == "Car or van availability (2011 Census) No cars or vans in household"] <- "NoCars"
names(msoa_copy)[names(msoa_copy) == "Ethnic Group (2011 Census) Other ethnic group"] <- "OtherEthnicGroup"
names(msoa_copy)[names(msoa_copy) == "Central Heating (2011 Census) Households with central heating (%)"] <- "CentralHealingPercent"



```
Let's now extract these to a separate dataframe, remove any missing values, and provide some quick summary statistics to identify any obvious concerns.

```{r}

feature_df <- dplyr::select(msoa_copy, RPDburglaryShifted, RPDRobberyShifted, total_burglaries, total_robberies, DwellingNoResidents, MedianHousePrice, FlatAprt, fullTimeStudents, NoCars, OtherEthnicGroup, CentralHealingPercent, AvHholdSz, ComEstRes)

feature_df <- drop_na(feature_df, RPDburglaryShifted, RPDRobberyShifted)
feature_df
```
```{r}
summary(feature_df)
```


```{r}

colSums(is.na(feature_df))
```
As a quick initial exercise, we'll create  a scatter plot of the interaction between each and every one of our variables. This will probably be too messy to make any real findings, but can serve to quickly highlight strong associations.

```{r, fig.width = 13}
pairs(feature_df)

```
As we hoped, some obvious relationships stand out: for instance, the presence of apartments, and households with no cars, or central heating and average household size.

Our robbery and burglary data and change rates are densely clustered - they're unlikely to cleanly associate with anything. With that in mind, we'll perform a log transformation. This cannot be undertaken with negative values, so once again we'll perform a shift (of 2) for both of our relative error numbers, as well as a commercial resident column, before log transforming our features.




```{r}
feature_df$BurglaryRPDTranform <- feature_df$RPDburglaryShifted    + 2
feature_df$RobberyRPDTranform <- feature_df$RPDRobberyShifted   + 2

feature_df$ComEstResTranform <- feature_df$ComEstRes   + 2


for (col in colnames(feature_df)){
  new_name <- paste("log_", col, sep = "")
  feature_df[new_name] <- log(feature_df[col])
}
```
```{r}

drop<- c( "log_ComEstRes", "log_RPDburglaryShifted", "log_RPDRobberyShifted")
feature_df<- feature_df[,!(names(feature_df) %in% drop)]



```



```{r}

feat_transform_df <- feature_df[,17:29]
orig_feat_df <- feature_df[,0:17]


```
We've now separated a separate dataframe where each value has been log transformed - while this isn't hugely rigorous (and would benefit from inspecting the relationships in more detail) it serves our immediate purpose.

```{r, fig.width = 13}
pairs(feat_transform_df)

```

While we've introduced a bit of noise, we've also "forced" some of our variables into relationships that look semi linear. 

To dig into this deeper, let's create a correlation matrix for our entire transformed dataframe.

```{r}
correlate(feat_transform_df)


```

To provide a visual aid, I've extracted the column for our robbery relative change rate, and sorted the table accordingly.


```{r}
dplyr::select(correlate(feat_transform_df)[order(correlate(feat_transform_df)$log_BurglaryRPDTranform),], term, log_BurglaryRPDTranform)
```
### Regression
Now that we've transformed our data, cleaned it up, and identified potential correlates, let's build our linear model. 

There are various automated tools for this process that seek to provide the highest fit and significance, but given the high degree of correlation between my chosen features, I've taken a more manual approach and tested a variety of models until I identified one with a suitable fit.  The final model is below.

```{r}
mod_burglary <- lm(log_BurglaryRPDTranform ~ log_total_burglaries + log_FlatAprt + log_MedianHousePrice  + log_ComEstResTranform, data = feat_transform_df)
summary(mod_burglary)
```

Our model suggests the largest burglary decrease linked to lockdown was in MSOAs which a high level of historic burglary. The composition of housing/accomodation and area type also seems to play a role, with those areas with higher median house prices, and a larger number of commercial residents, seeing stronger decreases, while conversely areas with large number of apartments temper the effect.

While all our variables are significant, the model is not a particularly good fit - the adjusted R2 is around 0.08, suggesting that less than 10% of the variance is accounted for by our model. I suspect more geographic features - such as distance from central London, more accurate footfall, or spatial lags - would probably be useful, but that's outside the scope of this project.

Let's perform a similar exercise for robbery.

```{r}
dplyr::select(correlate(feat_transform_df)[order(correlate(feat_transform_df)$log_RobberyRPDTranform),], term, log_RobberyRPDTranform)
```


```{r}
mod_burglary <- lm(log_RobberyRPDTranform ~ log_total_robberies  + log_total_burglaries + log_FlatAprt + log_CentralHealingPercent + log_fullTimeStudents, data = feat_transform_df)
summary(mod_burglary)
```

This is a notably better fit than our burglary model, with our R2 suggesting we now account for over 20% of the variance. The nature of our predictors is also quite different: while we still see a negative relationship with historic crime (with areas of high historic crime experiencing larger relative decreases), there is a positive relationship with both the presence of apartments and central heating.

I suspect some of these features are correlates of deprivation, so I want to create a quick scatter of three - for now we'll do it against median house price, which is definitely deprivation correlated.

```{r}

heating <- ggplot(feature_df, aes(x = log_MedianHousePrice, y = log_CentralHealingPercent)) +
  geom_point()+
  geom_smooth(method=lm)

apartments <- ggplot(feature_df, aes(x = log_MedianHousePrice, y = log_FlatAprt)) +
  geom_point()+
  geom_smooth(method=lm)

comest <- ggplot(feature_df, aes(x = log_MedianHousePrice, y = log_ComEstResTranform)) +
  geom_point()+
  geom_smooth(method=lm)



ggarrange(heating, apartments, comest, ncol=3, nrow=1 )



```

While there does appear to be a relationship with some of these, it isn't strong - this suggests the factor's we have identified are significant not because of their association with deprivation and poverty, but because of what they mean about the specific characteristics of the area.

### Random Forests

Unlike regression, random forest doesn't really on any specific type of association - instead, we rely on computing power, repetition and iteration to capture the very best predictor for our variable, in any combination. 

There are risks to this method: our sample size is smaller than I'd like, and this may lead to over-fit of outlier MSOAs.

It does mean we don't need to worry about transformations or correlations: we can return to our original dataset, and let the model identify the strongest predictors.

```{r}
# we remove rows where our main error is na or missing
rf_msoa_matrix <- drop_na(msoa_matrix_numeric, RPDRobberyShifted)

#then we repeat for any columns where value asre missing
clean_rf_matrix <- rf_msoa_matrix[ , colSums(is.na(rf_msoa_matrix)) == 0]


#then we drop out any values that directly predict our error.

drop<- c("burglaryActual","burglaryError","burglaryPercentError","burglaryPredicted","robberyActual","robberyPredicted","robberyError","robberyPercentError", "RPDBurglaryShifted", "RPDRobberyShifted")

#remove out selected columns
data<- clean_rf_matrix[,!(names(clean_rf_matrix) %in% drop)]


#automatically remove white space and make names r compatbiel
names(clean_rf_matrix)<-make.names(names(clean_rf_matrix),unique = TRUE)

drop<- c("burglaryActual","burglaryError","robberyActual","robberyError","RPDBurglary","RPDRobbery","robberyActualShifted","robberyPredictedShifted","burglaryActualShifted","burglaryPredictedShifted", "burglaryPredicted", "burglaryPercentError", "robberyPredicted", "robberyPercentError")
#drop<- c("burglaryPercentError","burglaryPredicted","robberyPredicted","robberyPercentError")

data<- clean_rf_matrix[,!(names(clean_rf_matrix) %in% drop)]


names(data)<- make.names(names(data),unique = TRUE)
data
```
We start with modelling our relative rate of burglary shift. We divide our sample into a training set which we'll use to train the model, and a test set we'll use to verify accuracy and validity.

```{r}
sample = sample.split(data$RPDburglaryShifted, SplitRatio = 0.7)
train = subset(data, sample == TRUE)
test  = subset(data, sample == FALSE)


rf_burglary <- randomForest(
  RPDburglaryShifted ~ .,
  data=train, 
  importance=TRUE
)

summary(rf_burglary)
```
```{r}
#calculate our predictions and a  rmse
prediction <-predict(rf_burglary, test)
Metrics::rmse(test$RPDburglaryShifted, prediction)
```

While machine learning models were once considered opaque and difficult to interpret, several libraries now offer functionality to explain predictions. Here I use [DALEX](https://cran.r-project.org/web/packages/DALEX/index.html) to do just this. 

```{r}

rf_explainer_burglary <- DALEX::explain(rf_burglary, data=train, y= train$RPDburglaryShifted)

rf_perf_burg <- model_performance(rf_explainer_burglary)
rf_perf_burg
```
We can see that our model significantly outperforms our best linear models: the R2 suggests that almost 85% of the variance is correctly interpreted, and our rmse (root mean squared error) is around 0.2 on our test set.

This model would be ill-suited to prediction or operationalising -it is a default forecast with no hyper-parameter tuning, and no consideration of error rates - but using tools like DALEX, we can identify which predictors the model identifies as most important. 

```{r, fig.width = 13}
model_parts_burg <-model_parts(rf_explainer_burglary)
model_parts_burg


```

```{r, fig.width = 13}
plot(model_parts_burg, max_vars=25)

```
The three most important features our model highlights are:
- the age composition of the population
- the number of residents which are in commercial property
- the historic number of burglaries

This seems to corroborate our previous regression model. To further unpick  these trends, we can use Partial Dependence Plots to identify how the model prediction shifts with these values. 

```{r}
pdp <- model_profile(rf_explainer_burglary)

```

```{r}
plot(pdp, variables="total_burglaries")

```
We still see a strong association between a high number of historic, and a large reduction during the lockdown period

```{r}
plot(pdp, variables= "Mid.year.Estimates.2012..by.age.0.4")

```
MSOAs with very large *very young* populations seem to have a less strong burglary lockdown decrease (though this is likely heavily associated to deprivation)

```{r}
plot(pdp, variables="ComEstRes")
```
```{r}
hist(msoa_matrix_numeric$ComEstRes)
```
By combining the distribution of commercial residents by MSOA with our PDP, we can see that those MSOAs that are most densely populated by commercial residents see the smallest "covid decrease"(suggesting that those MSOAs that are very heavily residential saw the sharpest drops).

```{r}
plot(pdp, variables="House.Prices.Sales.2008")

```

Finally, we can see that those areas that experienced the highest volume of house sales experienced the lowest relative decrease in burglary.

This highlights the importance of identifying correlates in RF models - especially in a dataset where features are highly interlinked, association does not imply causation, and we should be wary of over-interpreting.

We can now repeat our process for our robbery shift.


```{r}

sample = sample.split(data$RPDRobberyShifted, SplitRatio = 0.75)
train = subset(data, sample == TRUE)
test  = subset(data, sample == FALSE)


rf_robbery <- randomForest(
  RPDRobberyShifted ~ .,
  data=train, 
  importance=TRUE
)

summary(rf_robbery)

```
We've now trained a model.  Let's now use the DALEX library to understand it, and see how it performs.

```{r}

rf_explainer_robbery <- DALEX::explain(rf_robbery, data=train, y= train$RPDRobberyShifted)

rf_perf_rob <- model_performance(rf_explainer_robbery)
rf_perf_rob
```




```{r, fig.width = 13}
model_parts_rob <-model_parts(rf_explainer_robbery)
model_parts_rob
```

```{r, fig.width = 13}
plot(model_parts_rob, max_vars=25)
```

```{r}
pdp_rob <- model_profile(rf_explainer_robbery)
```

```{r}
plot(pdp_rob, variables="total_robberies")

```

```{r}
plot(pdp_rob, variables="total_burglaries")

```

The effect of historic crime effects again appears like a reliable predictor of a robbery covid shift: those MSOAs with the highest number of burglaries and robberies see strong decreases in robbery (though the association with burglary is not clear cut, suggesting other interaction effects may be driving this)

```{r}
plot(pdp_rob, variables="Road.Casualties.2011.2011.Total")

```
Road casualties is another strong relationship. This could be a proxy for deprivation, but I suggest this is more down to geographic features - road casualties are probably rarer in denser urban environments, most likely to be affected by lockdown.

```{r}
plot(pdp_rob, variables="Ethnic.Group..2011.Census..Other.ethnic.group....")
```
```{r}
hist(data$Ethnic.Group..2011.Census..Other.ethnic.group....)

```


Finally, we see a demographic predictor linked to "other ethnic group". I'm not clear how to interpret this, but it suggests that those MSOAs that are most diverse (and have the largest representation by these ethnic groups) experienced the strongest decreases in robbery during lockdown. 

Together, these analyses suggest that the crime drop for robbery and burglary during national lockdown was significantly affected by distinct local factors. For both offences, historical crime trends play a role, with high crime areas experiencing a relatively larger drop in both burglary and robbery.

Beyond that, the drivers vary for each offence  type: burglary was driven by the composition of the residential population, with heavily residential areas, and areas with a relatively "stable" population as measured by low housing sales also saw larger decrease - this is likely due to the increased number of empty residential properties.

Robbery decreases conversely, are well associated with high numbers of road casualties, as well as the ethnic makeup of the local population - this is likely due to an association with denser, more urban areas, with lower street speeds, and a possible link to deprivation, whereby minority population were least able to work from home, and were likely to still present as available targets for robbery.
